That's basically the next step to take, but beware, a lot of the integrated circuits in many newer pieces of equipment are NOT 5 V tolerant, so I strongly advise you power it up with +3.3 V first!
It has 5V marked at the connetor convenienly

.
Are there any voltage regulators on the digital board you can identify?
Can't find one. It is all 74HC logic and datecodes going back to late 1993...
By the way, is this instrument designed to be firmware upgradable?
Classic EPROM by the looks of it.
Don't rule out the possibility (if it is firmware upgradable) that it might have been bricked by a failed or botched firmware upgrade in the past!
Thanks for the hint...
If you can get sunlight on it at the right angle you might be able to see if there's anything intelligible in the way of characters or letters on the LCD!
I'll try that.
Otherwise it's just a matter of testing all the supplies on both the analogue and digital boards as far as you can, try and look for the system and microprocessor clocks (bear in mind there may be more than one clock signal in it – i.c. datasheets will help you identify clock pins!), and see if anything's stuck in reset or there's data/address lines either dead or stuck!
This type of modern equipment usually tends to hold calibration in EEPROM or flash memory, so once you've got it to operate, it shouldn't be necessary to recalibrate it – the very high maximum resistance this measures will necessitate calibration by the OEM or a specialist calibration lab with access to "T Ω" resistance standards!
Since this instrument won't be used for serious stuff I might cheat the calibration once the thing runs again (hopefully).
For the highest range it uses 1kV which I could relpace with a much lower external voltage and some 5GOhm resistors I have in a drawer.