I think Dell power supplies still use non-standard form factors. Even if the plugs match, a generic ATX power supply might not fit without retrofit. However, there are a couple of companies out there that make exact fit power supplies for Dell computers with higher wattage.
I have experienced several power supply failures in newer machines. In fact, we had DOA power supply in a new machine from the factory a while back. I think it is quite likely that you have dead power supply. Dell's power supplies leave alot to be desired...
Is your power button LED amber or orange? Depending on how the supply failed, you may be getting a power supply failure indication there. Also, most Dells have an LED on the motherboard that indicates whether the board is getting power. If this LED is not lit, you likely have a bad power supply