The easiest way to diagnose bad components and pick ups 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?"
My pickups sound great when selected alone, but sound very thin and nasally when both are selected. Why?
This is normally caused by humbucking pickups being wired out of phase. You can either switch the hot and ground connections on one pick up of flip the magnet to correct the out of phase issue.