The lock was jammed (not moving at all). I don't think stucked is the right word, it's just stuck. I got stuck with the problem (kept finding soultion but couldn't).

First, there is no such word as 'stucked'. Stuck is the past participle of stick. Jam implies two or more things blocking each other. A traffic jam is many cars, each one stuck in the traffic that is the other cars. A lock, clock, or other mechanism with many moving parts, can be jammed. Stuck describes something that can't move for whatever reason. It can be stuck with glue to something, or it can be stuck because of its position (in a rut, wedged between two things), or for a non-physical reason (stuck in the office, stuck at the airport because there are no taxis). Or you can be stuck on a problem because you can't think of the solution. None of these would be described as a 'jam'.