Sounds like a fault with the battery to me.
Have you tried removing the battery completely, and then running it off of the mains lead only?
EDIT: I see google lists this as a PC, so the above doesn't apply.
Usually on a PC the blinking light is an indication that the computer is in sleep mode. If it won't power up, try removing the power cable, and then hit the power button (to discharge electrics) and then reconnect, and try powering it up then.