no you can not make that change. the problem is that the XPS 420 is a BTX motherboard and not ATX standard. basically this means it sits on the left side of the case (from the front) and not the right side like an ATX board. to mount an ATX board inside it, would have everything flipped into the wrong place. the pci slots would be at the top of the case and the cpu would be at the bottom, so nothing would line up right.
you need a new case for ATX or mATX or any other ATX variant.
and yes i actually have one of those same machines in my house that still runs