First, make up a "grounding plug". That can be a standard "telephone plug" with wire soldered (wrapped, in a pinch) from the outer to inner conductors. Also, an old "guitar cable" can be cut down and the conductors expoosed and tied together (but soldering is better). The goal is an complete "short" of the input

Insert plug and turn on amp. A hum will now have to come from "inside the amp", not from a grounding problem or a damaged cable.