I just walked in on a Monday morning to find the Power Mac G5 off. Pressing the power button did nothing, although the power light was on. Pulling the plug for a moment did nothing either. Fortunately I found this technote from Apple which got things working again:

Power Mac G5 (Late 2005)
To reset the SMU on a Power Mac G5 (Late 2005) computer, either use the steps listed above for the Power Mac G5 (Late 2004) or:

1. Turn off the computer by selecting Shut Down from the Apple menu or by holding the power button until the computer turns off.
   
2. Open and remove both the metallic outer door and the inner plastic air deflector.
   
3. Remove the fan assembly immediately to the left of the processor module.
   
4. Press the SMU reset button on the logic board.
   
5. Replace the fan assembly, air deflector, and outer door.
   
6. Turn on the computer.