Sounds like your iMac G5 has the same problem mine has. Don't bother taking it to the apple store, they will just say your logic board is bad, and try to get you to shell out ~$500 for a new one. They said they tested it with another "good known" PSU, but I doubt it.

I took apart the PSU in mine, and I have one swollen cap, and 3 more leaky. Luckily I have friends who know this stuff.