I would start by wiggling all of the cables while they're inserted- if noise comes and goes, unplug them and use a multi-meter to see if you can duplicate the problem while you measure continuity. If you can, repair the cables and if not, replace them.
Where are you located? If you have constant hum, your local electrical regulations or the installation of the wiring may be part of the problem. If it comes and goes, you may have loose connections at the outlets, but that wouldn't apply if you can cause the problem by moving the audio cables.
What cables are you using, how old are they and are they bundled with many others and/or with power cables? ALWAYS separate power cords and cables and cables that carry signal and NEVER bundle them. Avoid positioning them so the signal cables are parallel to the power cords/cabling- it can act as a pickup for noise through the magnetic fields caused by current flow in power cords. Close proximity is your enemy, when this is concerned.
If the cables have been bundled with others and the jacks have been supporting the weight, the metal can bend and if the plastic around the center connection in the jack has broken (very possible), new cables won't cure the problem. If you have one cable that never makes noise, use that to connect to all outputs and inputs- if it still makes noise/distortion, look deeper into the equipment.
I don't think you have ground loops, I think you have damaged cables and/or jacks.