iMac 13,3 can't run diagnostics and is missing a serial number

I have an iMac 13,3 at my workplace that can't run diagnostics and is missing a serial number. It's running the latest version of Mojave.

First, the Diagnostics issue:

I've tried running Diagnostics by holding D at startup and over the Internet with Option-D. Both throw the following error:

Roughly a year ago, Diagnostics did work and threw the following errors:

4SNS/1/40000001:THOP—7.000 <-- hard drive temperature sensor

4MEM/62/40000000:0x7e63bf90 <-- memory

I did not replace any hardware. Could either of these errors cause Diagnostics to not run?

Now, the serial number:

I recently noticed there is no serial number in System Profiler:

The missing serial number prevents me from registering the iMac in Profile Manager which our school uses to manage our Mac fleet.

I've tried using the Blank Board Serializer to replace the serial number from the iMac base, but I get the same error message as I do for Diagnostics.

I'm not sure how the serial number went missing, but from what I've read, it might be linked to an EFI update gone wrong. Or not.

Could both of these problems be EFI-related?

Brian