Where to start repairing a faulty electronic board?
Diagnostics. 

In an ideal world the card developer provides you with a step by step test sequence to identify exactly which stage is faulty. Measure these voltages, look for this waveform, inject 1 kHz 10mV here and see 1 kHz 500mV there, and so on. 

If you don't have this - there is no service manual - learn the circuit well enough to develop your own. Keep one good card on hand so you know what it should do, and track the suspect card against it.

If you have a lot of similar cards, you can speed the process by making a test fixture, with connections to the test points and switches to connect them up to the test gear. Or even invest in ATE - Automated Test Equipment. (The original manufacturer almost certainly had an ATE setup programmed for this card, while it was being made)

This is all investment of course - how much time and money is worth investing in this process depends on how often you have to test it, and how valuable the working machine is...