Well, but then you end up with a beast sitting on your desk that sounds like an idling Harrier. I'll say this about Dells -- their cases are well designed to be quiet.
For what it is worth, though, I still couldn't bring myself to buy a Dell. My current machine was purchased with quiet in mind, and except for the stupid northbridge fan, it fits the bill nicely.
Now, back to the OP: As other people have mentioned, it is probably either the power supply or the voltage regulator on the motherboard. You're probably going to end up replacing one or the other. If you've got an extra power supply, try that first. While you've got the computer open, inspect the capacitors for leaking. Near the CPU, you'll see a lot of can-shapped things that look like batteries. The tops of them should be flat, with no evidence of bulging, and no stuff leaking out of them.
As WormGod suggested, computers die from heat. Heat usually causes the caps to leak or dry out. In either case, they stop filtering power right, which causes all KINDS of strange symptoms, until one day the machine won't even come on anymore.
Now, all that said, some people turn up some of the voltages to overclock the computer. I don't know much about that, though... I don't typically overclock, much.