Having the same problem on my G3 (Yosemite-blue & white). It restarts when I shut down. It also automatically starts up without touching a thing. There aren't any usb connections at all. For that matter, there really isn't any connections, except for the monitor, keyboard (ADB), and power. Have tried: changing battery updating firmware resetting motherboard resetting pram re partitioning and new os 9.2.2 and os X could it be the power supply? can I stick a pc power supply in a mac without any problems? thanks for any help.

Probably not the PSU, but just in case, XLR8yourmac.com has info about swapping in a standard ATX PSU... p

I have a small desklamp (with a 240V/12V transformer in it) plugged into the same outlet as my G3 imac. If I put the Mac to sleep BEFORE I turn out the light, it wakes up again! I thought it was probably generating a spike that was enough to restart the Mac.

Hrm. Might be. Stick an o-scope on the AC and see if there's a spike when you turn off the lamp. If there is, it sounds like you might want to get something that can isolate surges like that (a UPS, most likely) or put the lamp on a different plug, or just get a lamp that doesn't play tricks with your AC supply... p