The easiest way to diagnose bad components and pickups is to measure their DC resistance with an ohmmeter. Seymour Duncan has a list of DC resistances in their Tone Chart for all of their pickups. Potentiometers should range from their given values (500k, 250k, etc.) to zero and switches should read either infinite or zero ohms depending on their position. You can also use an ohmmeter to check your signal path and wiring or there is a non-ohmmeter method described in the section titled "I installed new pickups into my guitar and now it doesn't work, what do I do?"
WRITTEN ON JUNE 15, 2015, BY