It could be a dead power supply, hard drive, motherboard, or power on/off switch. What you're seeing is the reason why you need to keep backups on an external hard drive. If I were you, I'd take the computer to a service technician.
I'm currently posting from my Mac, however my PC is the issue. It has become entirely unresponsive, but I'm unsure as to why.
I'm really only a general web-surfer on this computer; I haven't done any experiments on it. Nonetheless, I turned it off one night and woke up the next morning to find it fully unresponsive. Nothing lights up or shows any signs of activity when I press the power button. It is plugged in and I have tried removing the battery and such with no success.
As I am almost exclusively familiar with Mac, there might be some simple fix, forced start, or other feature that I'm just not aware of.
This computer does contain some relatively important work documents, though, and it would be very helpful if I could access them again.