I'm sorry for the inconvenience that you have faced, I'm going to do my very best to help you, Steve_R.
Please let me know if you are able to use your keyboard and mouse once the NUC boot to the OS?
If you could run default setting on BIOS would be magnificent, however, the system is not recognizing the keyboard during post.
Could you try to disconnected the NUC from the AC power, remove all memory, SSD, etc. Also, disconnected the CMOS battery, and leave the the system without any peripheral for about 2 hours.
Then, try to access the BIOS again.
If after this procedure the issue persisted, it would be necessary to RMA the NUC
The following link will provide you the information for our Warranty department.