Usually, I try to pick all the low-hanging fruit first. That means, testing everything that can be tested without a deep-dive into the schematic and that is known to be a frequent source of problems.
In your instrument, that would be:
- The switches. Do they have all good contact resistance and good insulation?
- More general: Do you have low resistance on everything that is supposed to be connected in the schematic?
- Does the respective power supply voltage appear on all stages where it is needed?
Also, a thorough visual inspection is useful: Suspicious dirt anywhere? Corrosion?
An anecdote from my latest repair effort: The outdoor thermometer from my weather station failed, unless it gets completely fresh batteries. It worked and measured, until it had to transmit the data. Turned out that corrosion creeped into the cable from the battery compartment, invisible because of the insulation layer. Cable had several ohms. Almost no voltage drop during measurement, too much with the transmitter turned on. Lesson to learn:
Very often, the problem is in the connections, not the components. Like the one you just found in your meter.