There can be several issues.
Try this, unplug it, take out the battery, and hold down the "on" button for 30 seconds or so to drain the capacitors. Then plug it back in, and try to turn it on. (with or without the battery doesn't matter at this point). If that works (it's called de-gausing I think), then you might have to do it again several weeks or months from now. If that doesn't work, you probably need to send it out to have the motherboard "re-flowed", the solder connections inside can get loose over time.
HTH,
Gary