A quick check could involve opening the cavity, and move wires with something pointy whilst being connected to an amplifier.
This sometimes isolates the problem, if there is a loose connection or something. The wires to the jack is common, cut off 5mm or something and re solder. If still buzz, re solder all connections - checking the wires with a diode tester for continuety as well.
If it's still buzzing, you might have to check each component thoroughly.
Of course you have tried to replace/tested you instrument cable first..