I hate to be the bearer of bad news, but it really sounds as if you have a problem with a chip or two. The problem is, that just about every chip on this motherboard, with the exception of the Kickstart ROMs, are surface mount chips. That does not make changing the chips impossible, just harder. You need more than a soldering iron, in other words.
One point - when you do get this fixed, never, and I mean never, plug a joystick in with the computer powered up again!
I wish you luck.....