You are going to run into several problems.
PSU - While the wiring for the MB connectors may or may not be standard ATX, the bigger problem is going to be either:
A. The PSU is way underpowered for what you might want to do
B. A non-standard size/design/mounting
If you are lucky, the unit uses a standard ATX mounting. In which case replacing the PSU will not be a big deal, but you will have to replace it as Dell generally uses a low watt power supply. If it is not standard, finding one of higher rating is a real pain and if you do find one it is generally fairly expensive.
Your next issue might be with MB mounting.. there is no leeway. So if it is not an exact fit in size/hole pattern, there is no way to adjust. The other issue might be the I/O plate. If it is integral to the MB tray, you'll have to remove it somehow to get the I/O plate to fit.
The biggest issue is going to be the front panel controls. Dell uses a 34 wire ribbon cable to connect the MB to a PCB in the front panel. There is no way to get around it short of changing the switches, LEDs and any other front panel controls/ports to an individual wired set up.
In short, changing the MB from a Dell board to an off the shelf board may be a bit more of a pain in the ass if you want to keep the case than it is worth. Your best bet would be to get a case, MB/CPU, and PSU and transfer the drives and memory sticks to the new case.
Then you run into the problem of having to re-install the operating system to work with the new hardware. If it is OEM you will have to purchase a new key as the original is tied to the current MB and is not transferable.