Car won't start when I turn the key

Now that I think about it I hear some buzzing and clicks when I turn the key completely. If I push the car the engine starts, so I don't think it's frozen, because it also happened with the engine half warm, as for the lights dimming, I notice the clock dims a lot, goes from bright green to a dull green when I try to start, I also have an oil temp gauge, and that goes from bright white to almost turning off.
I might try tapping the starter with a hammer if I can get to it.

Clicking and dimming lights are a sure sign that the battery cannot supply the starter current, it could be

- a flat or worn out battery, my guess
- a bad connection on the battery, power cable and or earth strap
- it could be excessive current drawn by the starter motor

If you have access to a battery test meter, get the battery tested or failing that try recharging the battery or swap it for a spare.

Check all of the cables and battery terminals, make sure they are tight. Have you done any maintenance recently that might have moved or slackened a cable, earth or battery terminal?

You could try measuring the voltage on the battery under starting and see what voltage it drops to.

A battery under no load should read around 12.5-13.0V, may be a little more if it has just been charged.

Under starting a battery will go down to about 10V, the amount it goes down gives an idea to the battery charge level and condition.

If the battery voltage goes down below 9.5v on cranking, recharge and test again as below 9.5v indicates a very tired battery.

Below 9.0v under cranking means the battery needs replacing.

The battery is new, it's been replaced 3 months ago, it could be the alternator needs replacing and it is supplying just enough current to not trigger the battery light.
I'll have to get someone with a voltmeter to check the battery or buy one myself.
The ECU does inject some fuel though, because when it finally starts by pushing it, it surges up in rpms if I've tried turning it on with the key a few times.

Vandoni wrote:

I might try tapping the starter with a hammer if I can get to it.

Works great for Fifties era British cars.  But it isn't likely to be a helpful fix for your Jimny.

It sounds like you need to get in there and check/clean some connections.  Power and ground connections to the starter should be completely free of oil and corrosion.  Ground cable should be checked for integrity, new ones can be bought at any parts store (they are a generic item).  Haul the starter out, clean it inside and out and examine it closely.  Of just chuck in a rebuilt unit -- they're cheap. 

You didn't mention mileage but this is a very standard maintenance item for a car with some time on it.  IMO there is no need to look for low-probability issues here, though of course we on the board like to mention every single possible crazy idea.  (Stuck engine???  come on lads!)

 

There is a yellow light that's a car with a lock, but it never flashes and the engine gets fuel when I turn the key, because when it finally starts by push it surges in rpm

Yeah stuck engine sounds a little crazy ahah.
The car has 110k miles/175k Kms and 25 years, so yeah it was bound to start having these issues. It's not the first time it's happened, at first I thought it was the battery but not that's new.
I'll check the cables today, might just be a bad ground (?) or some grime