MDD G4s have an above-average rate of power supply failures. This article will help you diagnose the PS to see if it has failed:
http://www.jcsenterprises.com/Japamacs_Page/Blog/D275729F-09DA-4FBB-96B3-BEEEB2C 04619.html
Assuming the PS is OK, move on to the next suspect. The front panel board that contains the power button is also a trouble spot. With some versions you have to push the button "just right." Try pressing the upper right quadrant of the button, then the upper left. Front panel boards are still available on the used/pulled market and are not hard to replace:
http://www.dvwarehouse.com/Apple-Front-Panel-Power-Button-Board-for-PowerMac-G4- MDD-922-5276-820-1339-A-p-31929.html
If you think the FPB is at fault but cannot find a replacement, there is a possible workabout using an old iMac USB keyboard. The early iMacs shipped with the model M2452 keyboard, the only Apple USB boards that have a power button on the keyboard. A long-time Apple tech said the M2452's power button would override a dead button on the front panel board.