Mr. GJ:
You've identified that power is getting through the cord to the Mac.
Disconnect the keyboard from the Mac and then try the power button again. If the button lights, it would indicate that the keyboard must be replaced.
Try doing a "deep reset" (my term) and completely de-energizing the Mac. I don't have high expectations, but perhaps it's still worth a try:
Unplug everything from the back of the tower except the power cord.
Ground yourself by touching a metal slot cover on the back of the Mac.
Disconnect the power cord.
Depress & hold the start button for a five count.
Open the side door and remove the battery.
Reset the PMU, depressing the button for a five count.
Let the Mac sit for a couple of hours to drain the capacitors completely.
Reinsert the battery, close up, hook up and attempt to boot.
If you're handy with a multimeter, here's a detailed trickle voltage check you can run to determine if the power supply is okay or not, instead of buying a new one and hoping that it's the cause of the problem:
http://docs.info.apple.com/article.html?artnum=95064
Don't let the test scare you off... it's really easier than it sounds. You'll have to buy or borrow a multimeter, but that's a lot cheaper than a power supply that you may not need...
The other thing that comes to mind is the possibility of a bad front panel board, if the power supply checks out okay. Here's a link for someone's take on that issue:
http://www.smalldog.com/newsarchive/techtails_display.php?id=44
BTW - I'm uncertain whether or not the monitor power button, which you've ried to no avail, bypasses the front panel board's power switch or works in conjunction with it. I would guess that it bypasses it, but I'm just not sure...
Here's Apple's procedures for replacing these items, if necessary:
http://docs.info.apple.com/article.html?artnum=75312
Lastly, the logic board could be bad, but I'd eliminate the other possibilities before looking to this one...
Gary