Sounds like you have a grounding isue with your guitar - easily solved but you need someone who knows what they are up to. Bring it to a guitar shop and they should do it in a matter of minutes - all it needs is a soldering iron.
If you are getting the same problem using other guitars through the same gear (and assuming they are properly grounded) - you could have a ground loop...? Do you get the same noise if you connect to a different amp? IF you don;t have access to one, try connecting through a distortion pedal direct to your pc. If there is no interference then the problem is with your amp - my money is on groudning anyway, otherwise th enoise would't go away when you touch the guitar.