PowerMac G4 doesn't respond the switch on

You can replace a power supply, if you can still find one. I don't know about repairing it.

Another possibility is the PRAM battery. Those only last a couple of years, particularly if you leave the computer unplugged a lot. Most of that generation take a 1/2 AA 3.6 volt battery which is not the easiest to find. I usually order one from macsales.com but you can get one from Radio Shack or a Battery Store if you're willing to pay 3x the price.

Texas Mac Man's PRAM, battery, PMU tutorial - https://sites.google.com/site/macpram/mac-pram-nvram-cuda-pmu-battery-tutorial

Resetting your Mac's PRAM and NVRAM - http://support.apple.com/kb/HT1379

When to reset NVRAM or PRAM - http://support.apple.com/kb/HT1895

Are you using the button on the computer's front panel or do you have the older USB keyboard that has a power button? If you are trying the panel button with no joy, try the button on the keyboard if present.

Sometimes the button on the G4 front panel get wonky and either stops working or must be pushed a certain way to activate. Try pressing the edges of the button instead of the center, usually at the diagonals--10, 2, 4, and 8 o'clock.

The USB keyboards with a power button were model M2452. They may predate your G4-DA but the timing was close enough I thought it worth mentioning. The power button on such a keyboard will override a failed button on the case.

You can convert an ATX PSU for use on a G4...

http://atxg4.com/gige-da.html