I had good luck with a 2.0DP. The owner had the cooling system fixed under warranty but said it wasn't stable after that and gave it to me. I didn't look at it for 6 months then also has issues. Used my compressor to blow out a ton of dust and it's been rock solid since.
Yep it's almost guaranteed that the PSU is cactuar, and this will be the primary issue that prevents it powering on... However it is likely that it has logic board issues or will have them eventually. Unfortunately, the PCI-x G5's were complete and utter garbage. I have a 2.0DP that makes a good shelf for this reason... It's unstable and unreliable as hell, and sometimes dumps a CPU when it feels like it, rendering it only a single-processor machine. In the end I opted not to fix it and simply replaced it with a PCI-e 2.0 dual-core instead given how far the prices of 2nd had G5's have dropped. I can't say a bad word about this machine... it's fantastic, and appreciably quicker than the one it replaced.