Help! Mac G4 (MDD) will not start!

I have a G4 (MDD), OS X 10.5, that worked fine until yesterday.
Before going away for a few hours I put the Mac to sleep.
Came home, moved the mouse, nothing happened.
I pressed the power button, light flashed briefly, then went out and the fan blew loudly for many minutes.
I pulled the plug, waited 5 minutes, replugged, pressed button, same thing.
I opened the Mac, cleaned, removed battery, reset PMU. Plugged in, pressed button, same thing. Fan blows loudly, monitor is in power save mode, Mac stays off.
What can I do?

One year ago I installed a new power supply.

I'm writing this from a local public library, so it could be longer intervals for me to respond to suggestions. But I appreciate all the advice.

 

Thanks for the replies.
Problem is solved easier than I thought. I replaced the battery, reset the PMU, and the G4 runs again. Clean and quiet.
The only place where I can buy such a battery is 21 miles one way, that was the reason I posted the thread.

 

Whoopee! Today I have the same problem as described in the thread title.
I pulled out the battery, reset the PMU. waited about 15 minutes, reinstalled battery and it works fine again. I just wonder what the problem could be. Obviously, it's not the battery.

 

This problem happens when I use the Apple menu to put it to sleep. Hours later I move the mouse vigorously, but get no response. So I disconnect everything, open the cover, take out battery, reset PMU, wait and put battery back in. Then it starts and runs as usual.
I sure hope it's not the logic board.
The G4 has been connected to a Dell monitor since 2009 without any problems.

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Today I thought of re-installing the Leopard 10.5. But didn't do it because the installation requires a restart. I'm afraid it will not restart.