@Tdeve11, it’s a fantasy and any rules apply that you want.
Go to your Cat dealer and and find a group 27 battery that hasnt been activated and maybe there are other sizes there too,pour in the electrolyte and wait a bit you should be ready to go initially-Kevin
If your little troupe of survivors goes to a car dealer and finds new vehicles with disconnected batteries, probably a year or more. If they go to an auto parts store and find batteries that have not had the electrolyte added–indefinitely. (like kmccune said) You might also get some mileage (pun intended) out of starting a manual transmission car by push starting it after the battery was too low to crank the vehicle–but the battery would still have to have enough juice to run the fuel pump and electronics.
An old classic like an early 70s vehicle with points or early electronic ignition and no other electronics would probably push start with a much lower battery than something modern. You’d still need some juice though–it couldn’t be stone cold dead. (like in “The Stand” with the old Plymouth in the desert, which you have to have read if you’re into apocalyptic fiction)
Of course something with a magneto ignition would start with no battery–like something with a lawnmower or other small engine. I figure you’d get at least 5 years out of gasoline stored in underground tanks or sealed gas tanks. Probably a few decades out of diesel fuel, which is much less volatile.
@Tdeve11 … I will add a couple of factors here that bear explaining. In my particular experience, I was lucky that I had filled my gas tank in my stored vehicle just before leaving for Alaska and it was a 1985 model. If you stored a brand new vehicle…loaded with accessories… then the probability that it would still start after 18 months would take a nosedive. Gas deteriorates rapidly unless you add a fuel stabilizer or, as in my case, you have the gas tank full.
Thank you, all! I don’t have time to write more personal responses at the moment, but I’ve read all your ideas, theories and comments.
Thanks for doing all that thinking for me. I really appreciate it. I still have book three of the series to write, and you’ve given me a lot to play with for that novel, too.
But I did have to say to oblivion: Of course I’ve read THE STAND! Multiple times, in fact. 
Check with the battery manufacturers.
I have two passions, physics and scifi. Well, three counting women.
Anyway, nothing turns me away from a scifi movie faster than when the makers simply invent things to fill gaps. Good scifi creates beyond but is written around science as it is known at the time. Filling the details in by using bad facts makes bad scifi.
@Tdeve11: You might also like Hugh Howey’s “Wool” series and novels by other authors that have continued the project with his permission. A new twist on the standard apocalypse.
NYBo, if the battert was completely dead it wouldn’t start with rolling it down a hill, the engine would turn over but it would have no spark. However an old race car or motorcycle with a magneto would roll start.
Car batteries are more than 30 amp hours…My little lawn tractor battery is marked 275 CCA and 30 amp hours…They are more into the 50 - 60 AH range ! Where did you come up with that figure ?
I will definitely look up the manufacturers. In my research, I’ve found a Diehard commercial about the zombie apocalypse, so that was amusing.
https://m.youtube.com/watch?v=v-D7bJL8Tgc
And oblivion–of course I’ve read WOOL. 
And SHIFT. Have DUST on my To Be Read list, but haven’t gotten to it yet.
Thank you all again!