Sometimes my computer doesn't boot when I turn it on. As soon as I press the power button, the disc drive keeps spinning. Nothing comes up on the screen, not even POST. After I try to restart it a few times, it will boot and work normally. Most of the time this happens when the computer was RECENTLY on or I try to reboot it, but it never happens when the computer has been off for a long time, like when I turn it on in the morning. What could be causing this?Borrow a known good PSU of the same or greater wattage and swap it in there...

I've also seen this when a MBoard has a weak/failing cold solder joint on it...very hard to track down though.What's the age of the motherboard?
If you remove the RAM and start the computer without it, then no beep sound, you BETTER PREPARE for a new.

Follow Patio suggestion 1st, try with a know PSU with the same / higher Wattage.I'll try a different power supply when I can track one down, most people I know have laptops. The motherboard is around 2 years old, and so is the PSU. I can't try removing the RAM and listening for beeps because this computer doesn't have an internal speaker. What I find strange is when it DOES boot, it works perfectly FINE...Could be a overheating issue...

Get some canned air and a brush...and do a thorough cleaning of the inside...especially around the heatsink. Protect your computer from ESD (electrostatic discharge) and above all...make sure the computer's off and un-plugged while doing this.I just cleaned the computer a few days ago, thinking the same THING. Didn't fix anything though.