It could be electromagnetic interference which will be a hum or a buzz. It can be caused by the power source. If the power source is internal and it is a cheaper electric piano, this could be your problem. If the power source is outside the equipment (a black box attached to the power cable) move it away from the equipment.

Balanced cables actually won't have much benefit for an electric guitar, since guitars don't send balanced signals. You can use them but it only sends a mono signal so it will only be using one of the connections, I think. Plus, balanced cables are WAY more expensive.

Sorry I guess I missed that part. Well, keeping it away from electronics will definitely help. Anything that emits radio waves. Do you use this for playing gigs or is it just stationary at your house?