Hyundai Matrix ( Or Lavita in Asia) (1.6/gas/manual)

So here is the deal. My Hyundai has had this weird thing I noticed. It would sometimes start on the 2nd try for the past 2 weeks or so. It was turning over just fine just wouldn’t start on the first try. Just the 2nd or 3rd one. I described this earlier

Today it got worse. It would struggle to turn over. I’d try over and over again until I noticed some plastic or rubber smell and my colleague who was looking at the engine said there was a little bit of smoke coming out somewhere behind the engine.

So we had to push the car to start it. The car by the way runs flawlessly other than this. The engine is fluent and quiet as it should. Nothing misfiring and so on.

One thing for sure. It’s not the battery. I tried 2 different ones to be sure of that.
What would you try first ? I’m going to bring it for diagnostics but diagnosing a car in Norway is pain in the ass and very expensive because most of the time they just look for faulty codes and that’s all they really do. At the moment I’m thinking I should tell 'em to concentrate on the starter or corroding cables or something. Other Ideas ?

@ga4a89 I wouldn’t waste too much time on the starter or cables if it’s cranking over just fine

It is cranking over just fine, at the normal speed, correct?

Isn’t there a Hyundai dealer nearby?

You said "most of the time they just look for fault codes and that’s all they really do."
Who are they?
It sounds like “they” are either not very motivated to find your problem . . . or they’re not very experienced and/or skilled.

i would look for the cause of that smell. Check for burned belts, hoses and wiring, to start with.

Have you tested any of the things we mentioned last time?
By the way, if a push start works, that sounds like you do have a bad battery.
You said you tried 2 different batteries. Why are you sure they are in good condition? Did you test them? How old is your battery? 4-6 years is all you’re going to get, by the way.