Before going for a new motherboard, maybe this will work. It has worked for other systems...
- Get an external USB hub with its own power brick.
- Plug the brick into the wall and the hub into a rear USB port.
- Connect mouse and keyboard to the powered hub and boot.
- If things work, reboot again to confirm.
- Then, without disconnecting the hub from either wall or PC, disconnect the keyboard from the hub and connect it to a different rear USB port.
- Reboot
- If keyboard continues to work, reboot again. If keyboard still works, repeat the process with the mouse
- Reboot again when both are connected directly to the PC, but with the hub still connnected to the PC.
Assuming both keyboard and mouse now work when connected directly to the PC, power off and disconnect the hub from the PC and reboot again. If you're lucky, both will work now without the hub. But if they only work when connected through the powered hub, you have a relatively less expensive work-around.
Not sure this is the right board (refurbished), but check it out. And you can always call Dell Spare Parts.