iMac G5 may work "fine" with multiple blown (bulging) capacitors, or might fail to POST or exhibit problems with just one defective capacitor.
My iMac G5 (17-inch, 1st version) has 2 bulging capacitors on the mainboard and it works fine. I reccaped the PSU (also very important on those!) about 10 years ago, but the logic board had no blown capacitors at that time.
I used to own an iMac G5 20-inch (last version with DDR2 RAM, etc), and it was crashing all the time. Culprit was one blown capacitor on the board.