Computer fails to start back up after hibernating?

I closed my screen last night and went to bed. When I woke up this morning and opened the screen, it was completely off and the computer would not 'wake up'. So I tried to hit the power button to wake it up, the space bar, nothing worked. So I held the power button and rebooted the comuter. This turned off the computer (I heard it) but then it wouldn't turn back on. It is fully charged but the battery says replace soon. It holds significantly less charge but has never before affected the computers normal process... It is plugged in as much as possible at my desk to a surge protector and battery back up unit. The battery is the only thing I can think of... do I really have to go get a new one? The computer was purchased in 2008 so it's barely three years old. Thanks 😕

This computer also heats up to wildly high tempuratures... is that normal?