Desktop Computer will not turn on. Why not?

[JordanIB]

Tried searching but nothing quite matched what I was looking for:

The symptoms: For a few weeks now, I've been having off and on issues with my computer powering on. I'd press the power switch and it wouldn't do anything. Often it seemed like I had to give my computer a "rest" for a while after shutting down before trying to power up again. In the last couple weeks, this has morphed more into having to hold in the power button for a couple second, pushing it in a certain place, and releasing it quickly, and hope that the machine powers up. As of last night, it is completely dead. Push the button and nothing happens. No fans try to run, no beeps, no nothing.

Does this sound like I just need a new power supply?

In googling, I've seen people mention the motherboard LED, so I'll just say that the green LED light on the motherboard is on, if that helps to diagnose.

What else can I do to figure out the exact problem? I've read about trying to short the pins on the power switch or something like that, but attempting something when I have no idea what it means makes me a little skiddish.

Any help is greatly appreciated.