I bought an A600 off ebay earlier this year and when I got it home it would power on but all I got was a black screen. Then it decided to work and then seem to power down itself intermittently. I opened it up and there was a screw jammed where it shouldn't have been. There was also a screw missing from the floppy drive bracket, which of course was the one on the motherboard.
I'm guessing the previous owner had in the past replaced the floppy drive, used one of the case screws instead to secure the floppy bracket to motherboard, obviously the case screw is shorter and so it fell out of the bracket given time, and the correct screw is longer and he used that on the case so this 600 has a "nipple" from having had a long screw (tightened).
The floppy drive is really nice actually, a Panasonic JU-257A606P.
Anyway, I removed the screw, and it worked. So, check for a loose screw or something, something that may be short circuiting. You never know your luck. I was lucky it didn't damage the motherboard.