I actually solved my problem a while ago. I too thought it was the power supply, and took it to Best Buy, where for free they just plugged in a different power supply with no change to the computer. That left the internal connection, so I opened the case (which was quite easy to do) and the place where the power cord connects to the motherboard has a small silver housing. I just kinda wiggled mine around until the light of the power supply came on again, and put it all back together. No problems since.
Hopefully that might work for you.