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If that was the case removing the computer from the outlet and running it on battery would sort the problem?
On a guitar I guess even the person holding it can work as a 'ground loop'? specially if bare foot... :D
PedroPinto-
Yes, the guitarist can create a hum but usually when you touch the strings the opposite happens.
Your computer is not really running from the mains, it's charging and powering the battery. I would never have said your computer has no earth potential, even if the power supply has no earth the case is connected to earth. So all the time you only have one source of earth there is no hum, introduce another different source of earth and it creates a hum.
I'm not going to try and give you a definitive answer to why without having a close look at the equipment involved and running some tests but the problem is the potential difference between 2 pieces of equipment and it's a nightmare in sound engineering because different designers have different approaches.
Almost all systems have some noise, it's a question of how much gain you apply to it. Guitars/Mic Inputs/Phono Stages are all small amplifiers providing a lot of gain so they are a common source of noise.
Just to say I've built phono amps, amps and all kinds of micro electronics but don't pretend to understand them in any great depth. I'm also a qualified electrician but when I have the same problem as you I leave the thing plugged into the usb port.
Airhead
The computer is plugged into a power adaptor which may or may not have an earth connection. Good luck trying to solve this one. Sometimes it happens on stage, guitar processors are the worst. It's hard to do anything about it especially in a hurry.