Hum issues can drive you crazy. There have already been some good suggestions here but I will add a couple more things I have run into. These switching power supplies on computers, monitors, and accessories are notorious for leaking RF noise. Mix a dirty power supply with a little 60Hz magnetic field and it can put hum on audio circuits. Sometimes turning off and moving around power supplies can give you a clue if such a problem exists. Use shielded audio cables and keep them away from power supplies, monitors, cpus, etc. as much as possible. The other issue is any source of RF transmitter particularly on lower frequencies below 500MHz. Wireless microphones, speakers, baby monitors, etc...
Ground it, unground it, capacitive couple it, inductive couple it, shield it, move it around, and watch out for strong RF fields. Keep hacking away at it an you will eventually discover the cure.