Xbox will not power up, power supply light is orange, no POST

Hello, I have an Xbox 360 S that is having issues. One night while watching Netflix, the whole thing just shuts down. No power. So, I try all I can, the first thing I thought is that the Xbox overheated, and it was only mildly warmer than usual, and there was no overheating error code on the screen. It was just fine to a black screen. The power supply's light is orange, which means the power supply is reportedly good, but I'm not so sure. Xbox Support said that it's a hardware issue, and of course they would be glad to take it in for the steep price of $99.99. I of course knew this was a ripoff, considering it is out of warranty, etc. So, this is what the console does now. The light on the power supply is orange. I go to turn on the console, and there is no POST. It receives power, the light turns green on the PSU, and then it shuts off again, not displaying the Xbox splash screen or anything. I have no aversion to cracking the Xbox open, considering it is out of warranty and probably needs a nice clean and repaste anyway.