I have two of these machines sitting at my house right now (dual 1.25GHz G4 MDD), both with dead power supplies.
One will start intermittently after finagling around with the power cord, PMU reset and PRAM battery. Shortly after starting, though, it will kernel panic, freeze, or spontaneously shut down.
The other won't start at all.
Both exhibit the symptom of pressing the power button and having the button light up for the duration of the press -- but after releasing the button, the light goes off. Through much research and a little blood/sweat/tears, I have deduced that the power supplies are bad (they are both Samsung-brand power supplies). This seems to be a common problem with this model of G4.
There are replacements available online through the likes of eBay, Amazon, etc., but they run up $300 or more sometimes. There are also guides available online for modding a standard ATX power supply as a replacement.
So, my vote is that your power supply is gone as well. Since these machines go used for around $200 to $400, it seems ridiculous to spend that amount on a single power supply -- it would be more economical to purchase a used, complete system!