Answer to "Can't power on, bad power supply or inverter?"It could be a shorted hard drive. The computer will not turn on of a component inside is shorted CD drive hard drive ect
Answer to "Replace the screen and iPod don't react anymore"Put the cracked screen back in and see if it works maybe the new one is a dead one
Answer to "System does not come on"sounds like a gpu problem but not sure. Id take it apart and see if you find anything obvious. Check all capasitors make sure there not discolored or buldging ontop. If you cant find that code anywhere on there website if nothing comes up on screen like it never turns on its probably your gpu. And you can reflow it if needed which is easy i do it to my laptop every couple weeks when my gpu craps the bed. It takes maybe an hour from start to finish. If you need to know how to do that let me know.
Answer to "Which Linux distribution would run on an older thinkpad r325?"I know the post is old but ill write anyways for anyone else. Mint and Ubuntu are the most new user friendly. The biggest thing when using linux the the graphics card. Linux can be very frustrating if it doesnt like your graphics card.