if you have been using it for a long period of time with the battery in it and plugged into the mains you probably have killed the battery, if your running from the mains for extended periods you should really either take the battery out totally (best) or pull the mains and run it on the battery for a while every week or so to keep the battery in condition.
Are you sure it gone into hibernation?
couple of things to try...
try holding the power button in for about 20sec to force a full power down and then see if it will switch back on
try pulling the power and removing the battery for 20min and then plug just the power (no battery) back in and see if it will turn on.
last thing leave battery out and power unplugged overnight and then try again with just power in the morning.
if nothing works may be time to take it to the nice man at the local repair place.