The power supply is a known weak spot in the Dell computers.
They save money by buying a PSU only big enough to get the computer out the door....so to speak.
It's a miracle that it lasted so long.
I replaced a blown PSU in a Dell XPS 400, less than a year old, because the user just didn't want to deal with Dell any more. This was his second RMA computer, from Dell.
I've replaced several PSU's in the Dell XPS series towers. You can buy a PSU tester for about $19.95 over the net, but that's wasted money if the PSU is just plain bad.
Or, if you have a digital volt meter, you can test the various voltages at the plug to the motherboard, but you have to activate the PSU by grounding one of the wires to make the PSU start up. I've owned a PSU tester for several years, so I've forgotten just which wire you have to ground. Opppps!
If the PSU in the Dell was, say for instance, a 300W supply, replace it with at least a 450w supply, just to be safe. Dell seriously overrates their supplies.
Good Luck!
The Shadow