Forum for G5
https://discussions.apple.com/community/desktop_computers/power_mac?categoryID=1 08
System Profile is in control panels or from upper left "Apple" icon "about this mac" and then "more..." there you will see the serial number of the G5.
Says what the model ID is like 11,1 and other items, that you have G5 2.0GHz perhaps.
You would be amazed at where and how much dirt and dust can get compacted and inside those units.
Schematic inside: http://support.apple.com/kb/HT1305
Resetting SMU may help if you have not tried.
How to reset the SMU on a Power Mac G5 (Late 2004) or Power Mac G5 (Late 2005)
Removing cables, power cord, RAM, and hitting power on button for 5-10 seconds, wait, return RAM and cables and attempt power on.
G5 in pictures for how to clean and take apart:
http://nysoyan.free.fr/Eaglefour/PowermacG5.html
There use to be years ago a power supply repair warranty program.
These are PSU parts I mentoned before - or if you want to go on ebay for one.
http://www.dvwarehouse.com/G5-Power-Supply-c-247_541.html