Suggestion: buy a power supply tester... $10-13US (see link below). It only determines integrity at initial plug-in, not how the psu will perform under load. For your current siduation though, it'll quickly and easily answer your question. Your issue could also be attributed to a dead mobo or incompatibility.
Just to clarify what CowboyTech's post... OEMs like Dell, Gateway, Compaq..ect. often remanufacture parts in their pcs (to cut costs). So it's quite possible that your pc will only accept Dell's own replacement parts.
And with regards to what MinorDamaged suggested, a multi-meter will tell you a lot more than what the tester will.
They're very common. Radio Shack has them, but they're a bit pricey. If you don't mind buying online, do a Google search and you'll find a ton of vendors. The link below has several models to choose from at very reasonable prices.
Hey, I found this ad;
hey, Ads are to be used= 1, to let people know its available
= 2, to sell something that can't sell itself
ULTRA-QUIET DELL PSU: SILENCER® 360 DELL
Our Dell-specific upgrade power supplies provide 30%-100% more power than factory Dell units. For Dell owners looking to add the latest power hungry video cards, optical drives or other high-performance components to their systems, our quiet and reliable Dell upgrade power supplies are the perfect solution.
360W @ 50C (400W peak)
.99 active PFC
+12V @ 21A
SATA drive connectors
Automatic fan speed control
Reduces noise by up to 90%