A non-Dell could be made to fit, however, as its a BTX there are very few commerciall BTX boards around. As it uses the Dell Proprietary and undocumented front panel connector, the user would have to be able to trace each lead out to find the correct leads and then fabricate the correct connector on the leads. The rear I/O panel would have to be cut out (it doesn't have a standard I/O panel insert) to accomodate whatever motherboard. I don't know about this model but many Dell's in that era did not have a standard motherboard mounting hole arrangement.
A refurbished Dell 5150/E510 motherboard is the best way to go. There were three different part number motherboards used during the production of the 5150/E510, and they are all interchangeable. The final production boards were 0HJ054 (I think that's correct).
Here is one I found doing a google search Dell DM051 Dimension E510 5150 Motherboard p/n:0WG261 945G