I see this is an old question, but I think I have another possible answer. I've read a lot of rubbish about fluorescent light noise, but haven't found the answer anywhere. I eventually figured it out myself. I hope this answer will help the next person who comes across the same problem!
It sounds to me like you've got either an earthing problem with your amplifier or an earthing problem with your home electrics. When mains AC passes through a transformer, the 'low voltage' side of the transformer is 'floating', and not connected to earth. This means that the '0Vdc' leg of the rectifier - which is connected to the guitar - will float at mains frequency. This doesn't matter as far as the amplifier circuits are concerned - all the rectifier voltages float together, but it does mean that the metalwork on your guitar will be floating round in potential at a harmonic of the mains frequency. This is where the hum comes from.
It a correctly designed amplifier circuit, this is easily solved: the 0Vdc in the amplifier is connected to earth. This stops the voltage floating, eliminating the hum.
If the amplifier isn't properly earthed, you yourself act as the earth connection - but only when you touch the metalwork on the guitar. That's why you get the hum when you're not in contact with the strings.
I would suggest that you start by checking your amplifier's mains plug: you should really have a three-pin plug with a separate ground pin. If that doesn't solve it, either there's an internal problem with your amplifier, or there is something wrong with the electrics in your house.