When I start the car the starter moter get stuck, just like the battery dead, but it starts with a little difficulty. Therefore the dead battery may be ruled out. can this be due to a faulty starter moter? If so where can be the fault?
This is really frustrating. I have 2 such situations, and after ruling out the battery and the alternator, it turned out to be the starter in both cases.
Mechanics call theis a “flat spot”, where the car will start intermittently. If it’s a standard shift, a little push will often get you started.
Have a good mechanic take a hard look at the starter circuit, connections, etc. You may be in for a new(rebuilt) starter. But it could be dirty connections as well.