It may or may not be compatable - sorry, can't tell. Or, you may have an assembly issue.
The mobo looks like an ATX (not a BTX). If the back panel and the expansion slots lined up correctly with the correct openings in the case when you assembled it, then at least the form factor is correct.
Many Dells have circuitry that lights up a series of 4 diagnostic leds on the case front panel. Your old case may have them, but your new case doesn't.
As Joe said, some older Dells had proprietary PSUs and mobos. Don't know about your system, but I tend to doubt this is the problem.
Did you have to install the mobo standoffs in your new case, or were they pre-installed? It is critical that the standoffs in the case line up with screw holes in the mobo. If not, the board will likely short out and not start.
Did you plug the start switch leads on the correct pins of the front panel header?
Did you plug the 20/24 pin and 4/8 pin connectors into the mobo?
Were there any wires you disconnected while removing the mobo from the Dell case that had no counterparts in the new case?
Just some ideas for you to consider - hope they help.
Can't find a review on your PSU, but it's not one we would recommend. [strike]If it worked before the case swap, it should be OK afterwards.[/strike]
Edit: The PSU is new.