Then @Whitey, the obvious approach to eliminating electricity from your transportation needs; get a horse.
Even fiction needs an element of realism to be readable. This really has little. It is a non “starter” ( to be coin a pun) in today’s society. There is no practicality and the inefficiency makes it a “cartoon” of an idea.
" get a horse"
You must be watching ‘Revolution’…
I don’t have a problem with the OP’s idea, his main character has ‘electron cooties’, it seems…the rest just follows…
If you read carefully, OP 's original post and all of the qualifiers on the cars he talks about, a simple response is, NO ! ALL cars he refers to cannot run without electricity. The opportunity to suggest any alternatives require more, not less, electricity in the chain to get to a car that does not. The logic if the exercise still evades me.
For the purpose of the story :
This could be one of those people ( there are many among us ) who can not wear a watch. There’s something about their body chemistry or electro-whachamijigger that stops a watch from working.
This person has an extra strong one of those. Whatever that is could be your ‘‘almost’’ scientific fact
that could make it believable-ish.
In the story, perhaps he could stumble accross different means of controling or subverting his electro-malfunction. Little things like ;
Swallowing a BB and quarter inch washer allows a certain brand vehicle to start…today ;
a piece of foil over his left ear will allow the windows to work ;
clenching a paperclip in his teeth allows a left turn ;
Silly little quirks like that when, once accidentily discovered , allow him to control or adapt his ability.
When I search ‘‘why can’t some people wear a watch’’ , I don’t yet see a name for it but I do see it’s very common and not so far fetched for this character.
And then , at the end of the story, he discovers that his electromagnetic energy is harnessable and with a couple jumper wires situated ‘‘just so’’…a non-working vehicle can be energized to work… off of him.
I guess @dagosa won’t be buying the book… But in his honor, the main character will ride a horse at some point in the book!
Seeing as how reality faded from view in the rear view mirror, I might throw this well thought out, or loopy, idea out there.
What about a diesel engine with a cartridge start; a la aircraft engine? I’m sure many have seen Jimmy Stewart burn through some of them on the C-119 in Flight of The Phoenix. Maybe the heat from the cartridge would be enough to heat up glow plugs (special material maybe?) enough to where the engine would fire off.
Of course, getting oil out of the ground to manufacture diesel also requires electricity but that’s another issue.
Post when the book goes on sale. I’m a huge science fiction fan and I think that I’ve read everything that Ray Bradbury and Isaac Asimov, along with others, ever wrote. 
As a young lad spending summers on a farm I recall being sent out to do some mowing on some kind of tractor from the late 30’s or early 40’s. It was a diesel engine and was a crank start. It had no glow plugs. It had a diesel fuel tank and a one gallon gasoline tank. There were levers to switch the fuel supply. You turned off the diesel and turned on the gasoline, cranked like a SOB to get the thing to sputter on gas, then manipulate the fuel supply as it warmed up and gradually switched it to the diesel tank.
As a 13 year old I wasn’t nearly strong enough to crank that thing over by hand. My big burly farmer uncle could crank that thing for 4 revolutions though.
It did have an electric starter but that unit gave up decades earlier and uncle saw it as unneeded.
Y’all musta been raised mighty rich. Well, I was raised mighty po’. When we had a car or tractor which wouldn’t start, which was often, what with bein’ po’, WE PARKED IT ON A HILL!!!
There, wasn’t that easy?
In fact, in my insane young male years, I had a 1953 Chevrolet, known in those days as a Babbit slinger. I wanted to go much faster than 1953 Chevrolets do. So I took the fan blade off and tossed it in the trunk. Then, I took the oil bath air cleaner off and threw it in the trunk. It sounded really cool at full throttle with that cleaner missing.
Then I loosened the clamp on the distributor thingie, and turned it to maximum rpm at idle. That old man’s car all of a sudden would run 35 in first gear, and over 65 in second. Just before I got drafted, I made 96 (indicated) in high on a long, long downhill run.
The only problem was, it would not start on the starter. I had to park it on a hill. If I messed up and shut if off not on a hill, I had to go up, raise the hood, and twist the distributor thingie back long enough to get it started. Then, tune the distributor thingie for maximum rpm again.
Some one is going to point out running a babbit machine like that is probably not good for it. Just before I left for the draft, I drove to Arkansas and back. it took me 40 quarts of oil, a quart every thirty miles. I came back in December 1964 and put in a rebuilt motor and transmission, and drove it 2050 miles to Ft. Lewis in 50 hours. It kept me through my service until I could afford a new car after I got married.
So, put big hills in your story and mechanical diesels. But, he won’t be driving after dark with no headlights, unless he has acetylene lamps.
I do believe that MikeInNh is right and this is for what it's worth, a way of demonstrating how important electricity is and not a way of actually replacing it.
I’m NOT saying he should demonstrate how important electricity. I’m saying it’s important to come up with a scientific plausible explanation as to how it could happen. If not it’s just pseudo science.
Just the idea that all the possibilities are not only inconvenient but overly expensive and require more preparation and backwards technology and ALL have to be supported by more energy expenditure then it’s worth, undoubtedly by the use of electricity makes this exercise…( fill in the blank) . It would make more sense just to write a fictional novel in another pre electricity dependent time frame. There is no present day scientifically plausible explanation of how this could happen and be of any use other then a one time demonstration of something totally useless.
…Just to answer your original question OP, again. NO !
And, if this does not demonstrate how important electricity is in everything, let alone transportation, I don’t know what does. To inlude this in a fictional novel that I hope would have some semblance to reality, would be totally contradictory. And, as @irlandes points out, you couldn’t drive it, license it or even get away from being ridiculed for owning it with the intent of using it for practical transportation. Develope a new story line !
Dag, you must have been a real bummer, comic-book-wise…
Didn’t have time to read all the posts,get an old direct injection Mack truck.with mechanical injection and an air starter-a little rough but you would have wheels-Kevin(they start fine above freezing with direct injection(avoid prechamber motors)
I have driven tractor trailers that required no electricity to work. Their fuel pumps were engine driven and they could be set on manual. You either had to stall them to shut off the engine or some of them used a manual fuel shut off valve. You would need one equipped with an air (compressed) starter. I have never seen a diesel you could hand crank. Some of the early ones needed a compression release so that the started could crank them.
Also, in Montreal, I saw a driver stranded at a motel with an old 220 Cummings engined tractor that wouldn’t start at -25F wrap a tarp around the bottom of the tractor and build a wood fire under the crankcase to heat the oil to get it started.
@dagosa, I’m surprised to see you react this way to creative fiction. Do you tell little kids that Santa and the tooth fairy are not real? Do you ridicule children who have imaginary friends? Is there not a creative bone in your body?
I have the same aversion @Whitey to presenting any fictional novel ( not cartoon, not Santa, not the tooth fairy ) in a way that doesn’t bear any semblance to reality. I know Mad Max scinereos are very entertaining but, I did not know this forum was engaged in literally prose. I am just supporting my point of view as a response to OPs original supposition and question with an emphatic No ! as he was asking a real qestion that desearves a real answer…it isn’t going to happen, and you can’t run a modern car that way it’s not reality to pass it off that you can.
Steven King, once a co worker of mine, gets the same treatment. Originally very entertaining but often not reality based often and one time viewing or reading is enough for me on many of his stories.
IMHO, it’s not creative fiction to completely change reality. It shows a writer’s research and dedication to realism by accepting reality and working within it. For example; the movie " Contact" is good creative fiction because though it seems far fetched on the surface, but it is entirely reality based from what was known at the time of inception.
There are too many movies that disregard reality from the way violence is portrayed to the way “cars” are portrayed. If you want to NOT delve into mechanics, or physics and just protray it with out trying to actually explain why cars run a certain way ( without eectricity) under certain conditions, then just call his car " Chistine" and let it run on fairly dust. That i can see. But, don’t look for a reality that dies not exist as a premise for a novel that can’t be true.
It was said succinctly earlier by " shadowfox"; even humans can’t exist without electricity.
So Dracula, Frankenstein, 2001, etc. are off limits?
There are too many movies that disregard reality from the way violence is portrayed to the way "cars" are portrayed. If you want to NOT delve into mechanics, or physics and just protray it with out trying to actually explain why cars run a certain way ( without eectricity) under certain conditions, then just call his car " Chistine" and let it run on fairly dust.
It’s either sci-fi or Fantasy. This sounds like it’s sci-fi…but without the physics…it just becomes fantasy. Not saying that’s bad.
The shows written for the Sy-fy channel are strictly fantasy. They have NOTHING to do with Sci-fi…thus the reason they changed their name.