First. Try unpluging from charger, remove the battery, wait 5 minutes, put charger and battery back in, and the try again. This will reset the SMC, which might or might not help. see http://support.apple.com/kb/HT1411
Second, could be the charger or battery at fault, try each one individually (reset the SMC again before you try each one.)
Third try holding the power button down for a few seconds, this has worked for me in the past.
Fourth. The power supply circuit, or some other part of the logic board is broken, only option is repair or replace