First thing to try is resetting the power management chip.
Apple says: "The Power Manager is an integrated circuit (computer chip)...on the logic board of the PowerBook and iBook"
Unplug power, remove the battery, hold the power button down for 10 seconds.
Put the battery back in, plug in to power, turn on (single press of the power switch).
If that fails, onward!
There is a chance that the battery is helping to cause the problem. Any chance you could borrow another battery to try?
Replacing the battery, or, even better, having it "re-celled". I can not find the link at the moment, I had one for a place which recells Mac batteries...
Try press & hold <control><command><power>
Release, wait several seconds, press power.
http://support.apple.com/kb/TA25686
There are some reports of this working, probably for a different model
Try <control><shift><power>
Release, wait several seconds, press power.
http://en.kioskea.net/forum/affich-31408...
Also - Press & hold power by itself for several seconds (that is force-power-off command, so I doubt it will turn power on).
You can not reset the PRAM without turning on the machine, so PRAM should not be able to prevent power-on!
Anyone care to start a guide for recelling (not reselling!) Mac batteries?
I am tempted to suggest the Genius Bar...
Make sure you tell them about everything you have replaced if you do take it in.
I thought I could add more to this, but I got nuthin' now...