The fact you say it's fine when you move the cable away from the chassis, sounds like a grounding issue.

Are all the earth straps/wiring in good condition?
The first thing I'd do, is go around the chassis and check for any earth wires that are missing (look for remains of connectors underneath bolts/screws with nothing connected) or damaged wires. Any wires you do find, unbolt/screw them and check they're making good contact with the frame.
Check that the main earth wire in is good.

It migt talso be worth checking with a multimeter, that all the major metal parts have a good connection to the main earth terminal. You should see less than a few ohms resistance, anything higher and I'd be looking to find out why.