A micro-ATX board should fit, but you may need to change some of the female case wiring connectors. (You can get these from Front-X by mail order.) Also, you would be in violation of the Windows OEM license if you reactivated your OEM product code using a non-Dell motherboard.
I installed an Asus Core i5 in an XPS 7100 case (similar to yours) and that was my experience.