If a USB keyboard works then that would indicate a hardware problem. Especially since the keyboard does not work in the BIOS. I would not suspect the MB as much as a keyboard purchased off eBay. Have you thought about purchasing here as keyboards are genuine Dell and in most cases brand new.
I have a real head scratcher.  A staff member has an e7450 and has used it for several years without problems.  A couple of weeks ago the built-in keyboard stopped processing any key strokes from the keyboard, except for the "eraser" mouse button and the keyboard mouse keys.  The touchpad works.  The keyboard does not work while in the BIOS utility.  I can use an USB keyboard with no problem.  The on-screen keyboard works.  As mentioned the "eraser" mouse pointer and the three mouse keys work. What I have done: Removed the battery for 15 minutes; reseated the keyboard cables; flashed the BIOS to the latest version; ordered and replaced the keyboard; ordered and replaced the system board.  No joy! With replacement components my logic was, since the USB and on-screen keyboards worked, replacing the keyboard would be the fix.  When that step didn't work, I ASSumed that the system board had a bad keyboard controller, so I replaced.  Still no Joy! What am I missing here?  What are the chances that either the replacement keyboard or system board (both sourced from eBay) have the same problem as the original?  I have looked through this forum and others without finding this situation, only issues with some keys not working...not all of them. Thanks for your reply.
e7450 built-in keyboard not working