Do a search for ATX pinouts +Dell and you'll see. The plugs are the same. The wiring is not.
You can put in a standard ATX PS and continue to use the case if you really like it.
Things to look for then:
ATX backpanel positioning.
Expansion slots. Ex: The 4550 I got my mom doesn't have 7 expansion slots in the case, put a standard board in there and you'd have no way to use the ATX slot without cutting a hole in the back of the case. Might work with a Micro-ATX board, dunno, got it, looked at it, gave it to her. Wasn't my toy. Don't know what the XPS t600 case is like, just thought I'd point this out as something to look at.
LED/switch wiring is a nuicense, but wouldn't prevent you from reusing it.
Really I'd just buy a new case too, gotta get a PS anyway. Dells are nice for 'buy it, use it, toss it' and if the initial price is right like some of their recent deals it makes sense to forgo the upgrade path to get a nice system on the cheap. But they're not great upgraders.