CASE
After 2 hours of working, My Computer Suddenly Shutdown and wont power. The power LED was on, but there was nothing on the screen.I shut my computer off, and since then I have been unable to get it turned back on. There is absolutely no response when I press the power button.
I am at a complete loss as to what the problem is, but I don't think it's the power supply. My computer would run just fine when I wasn't using the usb port, but suddenly restarted while I was in the process of transferring music. Another thing to note is that I have transferred music to that exact mp3 player before under the same exact circumstances, with no problems at all.
Anyone who may know what is causing the problem, if you could please help me I would greatly appreciate it. Thank you.

SOLUTION

If I were you I would not turn on the computer again until you have a new power supply - in fact ATX power supplies are always powering the ATX mboard in some places, even when Windows is Shut Down or in Standby or Hibernate modes, and PS's can fail even in that state and possibly damage your mboard and anything connected to it - unplug the computer, or otherwise remove the power to it!

Failing power supplies can cause all sorts of strange symptoms and error messages, usually because of too high or too low voltages, but more importantly, the damage they can cause while failing is random, and you risk damaging your mboard and anything connected to it if you continue to use a failing PS, especially if it is producing voltages that are too high or it shorts.

You should have demanded that you got a new power supply after your PS "exploded". A power supply that does that is definately defective, even if it didn't "blow up" when they tried it. If it was a new PS, the vendor would have no problem getting the defective PS replaced by the manufacturer or distributor they got it from. If it was a used PS, it's a matter of buyer beware - you should have gotten another PS even if they wouldn't give you a refund.

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There are lots of el-cheapo power supplies out there that are likely to fail early and/or are more likely to damage your system while failing. Steer clear of the cheapest ones. It should be a brand with a good reputation, it should have a warranty of at least a year, preferably three years, and it should have anti-short and overvoltage protection built in (it will shut down in those circumstances).
If you are looking for a PS online, don't just look at the selling vendors info - check out the manufacturer's web site for that model - make sure it has a decent warranty - if there is no web site, or the web site is poor, look elsewhere.

How do you tell if the PS is malfunctioning or dead?
The best way is to borrow a known good PS with enough capacity and try it, or try your PS in a working computer.
Make sure all the wire colors and numbers of wires on the main connector from the PS are the same - if they are not one PS is not compatible with the other!
If you can't do that....
take it to a computer repair place and have them try another PS, or.......

If the computer will not fully boot or the PS will not start up, or the computer re-boots or shuts down for no apparent reason......

Sniff the PS fan outlet area with the power off - a strong burnt wiring / burnt plasticy smell indicates the PS has been overheating or has been malfunctioning, regardless of whether the PS fan is spinning properly.
Try turning the PS fan from the back of the case with a pencil or something slim - it should move in jumps, but be easy to turn - if it is harder to turn, the fan is spinning slower than it should or has stopped spinning, the PS has probably overheated and damaged itself, and the PS is probably in the process of dying.

Look in your bios Setup at the current voltages (if you have the monitoring chipset for that) - +3.3, +5, and +12 volts should be within 10% of nominal values - your Vcc (cpu core voltage(s)) should be within 5% of nominal value(s). Voltages that are too high can do a lot of damage in a short time.

The PS fan should be spinning at the speed it is supposed to be - some spin according to how warm the PS is, slower when cooler, but it may not have that feature and in that case would spin quite fast. If it spins too slow or has stopped, the PS will overheat and fry itself, malfunction for a while, and eventually die.

Some PS problems only show up intermittantly, or only when you add an additional load to the computer - when the computer is booted, or when you are running something that stresses it more, such as when you are burning a CD or DVD, or playing a recent game.
You could try installing a mboard monitoring utility that can monitor your temps and voltages in Windows, and set it up so that it is monitoring all the time and will warn you if something goes out of whack, particularly the voltages.