Does the display show a fixed reading or is it "measuring" (ie, the value is chaging) but without any correspondence to the input?
If the former, I would check if the trigger circuit is working correctly. If that is rueled out, perhaps inject a signal internally past the analog front end, at the input of the ADC (and do the reverse too, measure what signal is there when you apply an input). That way you can rule out any of the analog frontend parts.
The fact that the display is working seems to indicate the main MCU is fine. If the problem isn't in the analog frontend, check if the optocouplers that connect the ADC to the MCU are doing ok. This was where one of my units had a problem (with optocouplers, in my case it wasn't an opto related to the ADC but to the front-end switching).
If it is the front-end, check those optocouplers and check what relays should be switching for different ranges. The service manual covers this in some detail and should be clear in combination with the schematic that is also available in the service manual.