Whin I had this problem i ended up changing out my backlight board and that made the screen go fro pitch black nothing on to blue everything is shiney and working. Not saying that is your problem, butt you can find some on eBay for around $40.
Probably check all your cables connections going to the power supply. If that doesn't reveal anything take the power supply out and check for any burnt spots, or blown compasitors. and try another wall socket. Also check that the power button is working right.