My Mac Power G4 Went to sleep and I Can't Wake it Up!

Question

Must have felt I didn't love it anymore.
I bought it so long ago, I can't remember when — only that in the interim I've also acquired a Mac Notebook, an IMac that eventually "wore out" and a duo processor iMac to replace it.
Still, I've also kept my G4 running and networked to whichever iMac I was using at the time — mainly to maintain a way to view and revise older docs running on OS 9.6(?). But as time rolled on, I used it less and less, until this morning, when I realized an old tax document I needed probably was on that computer and realized it hasn't be working . . . probably for weeks or months.
To my dismay, it won't start up (from either the power button on the keyboard – or the computer itself. Have already tried unplugging and replugging it from the wall, but it still won't turn on.
Before I run out to buy a new power cord, just anted to check to see if there might be a different problem (e.g., dead power pack?).
It's been a great workhouse, so I'd hate to lose the machine, but if diagnostics and repairs are as high as I'm guessing, I know it makes more sense to just replace it with a newer model.
If so, although I've also just rotated new models in as my primary computer and kept the former "top model" as a back-up, I'm wondering if I might not be better off just buying one of those stripped-down models for sure as a back-up. Then again, my current iMac must be 4-5 years old.

Answer 1

I promised to let you know if your suggestion worked. Sorry it's taken so long, but today was the first time I had a chance to try it out . . . and then, only because I need a document I believe is on that computer.
The sad news is that after I removed the battery (and let it sit close to 20 minutes before replacing it) my Mac still did not turn on.
Next I started the search for a new battery. Was concerned about buying one online, because they looked pretty pricey and I wasn't sure I might not have a more serious problem. Called the Apple Store, which was a real eye opener. The guy who answered my call on the national line didn't have a clue, so referred me to the local store. The girl that answered there informed me that the store doesn't carry batteries for such old models (good thing she couldn't see who she was talking to) — butshe was right, it is old (according to the serial #, I bought it back in 1999), but so far it's outlived the CPU that replaced it and until recently was keeping up with the first replacement). She recommended a Mac Genius appointment for diagnostics. No charge unless I decided to have them work on it, at which point it would cost $129.00 . . . but she didn't know if they had the battery either, and if they did (or could order one), she was not allowed to discuss merchandise costs on the phone.
The kid I spoke with by phone at Radio Shack didn't have a battery either, but thought they ran around $40. . . The service manager at Fry's thought that was a gross exaggeration, but could only find 3.0 v batteries when he looked (for only $4.99).
As a latch-ditch effort I called our local electronics store. They had the battery, but would be closing in about 23 minutes. I arrived just as they were closing their door . . . raced home thinking of all the $$$ I had saved and promptly insertd the new battery.
Result: Nothing. It's still dead as a doornail.
I hate to even imagine what else it could be. Is it time to junk it, or is there any hope left . . . and if so, at what cost? Changing a battery is within my comfort zone. Anything more and it probably will have to go in for service. Is it worth it?