What new motherboard can I put into a Dell XPS 420? Why keep the XPS 420 case? So my wife will not see a new case and know I s

The 420 is a BTX form factor, so start your search with that. You should also consider upgrading the Power Supply Unit, especially to ensure the P1 connector reaches the socket on the new motherboard.

Another thing to consider is that the front panel of the 420 chassis is a proprietary design, which means that all of the front panel connectors are attached to one large coupler to fit on to the 420 motherboard only. You'll have to find a way to splice new connectors on to the wire ends, after you've removed/cut of the proprietary connector on the motherboard side.
 
The motherboard in a Dell XPS 420 uses the short-lived BTX form factor, so I'm doubtful there are any better/newer motherboards that will fit in the case. Also, Dell is known for sometimes including a proprietary psu connector with a different pin-out than a standard ATX12V psu, so even if you find a motherboard that fits, you might need to change the psu as well.