Partly in reply to tmlab.
I've re-opened my MN5127 (I was getting busy on a Hameg 203-6 but easily get sidetracked, I just enjoy cluttering-up with works in progress...)
Here too main PCB will not run without GPIB connected, it just displays "---" too. I can't really see the reason for that either, as the manual does say that GPIB board is optional.
I tried looping Tx and Rx on main PCB (J6, 4-5) same display.
Tried removing NVRAM from socket on GPIB, that does not stop the DMM from working. So that more or less rules out my idea on a low NVRAM battery causing problems.
I had a quick look at the bus, (no captures, didn't pull the DSO out) the main seems to query GPIB on power-up, GPIB responds briefly.
After that main transmits data regularly to GPIB (likely measurement data for DAC on GPIB to feed the analog output), communication in the GPIB->main direction is silent (Rx remains high).
Your burnt tracks on primary side are quite surprising, any chance it was hit by a lightening spike? Unless it was saved from a H.V. test lab (the military have such a place in the south west of France) Do you remember any arc marks across the isolation before cleaning (around opto's maybe?)
Try focusing on the CI10 (GPIB µC), reset sounds good, but beware of it as /RES power on reset is based on a tantalum drop and these can get very "scratchy" with age.
Check oscillator, then that data reaches pin 12. (You'll have to power-cycle, main PCB only tries once on power-up, it drops Tx if there is no response from GPIB.)
There's only if CI10 is fried that you're going to have a lot of trouble saving the DMM.