There's a few simple tricks to try to see where the problem lies that you may already know...
With the amp switched on and the lead plugged in, but not the bass, touching the tip of the lead jack plug should produce a buzz from the amp (assuming the volume is turned up a little...). This eliminated both amp and lead; if there's no buzz, leave the bass alone.
With the lead plugged into the bass, and the amp switched on, (and a little volume...), open the control cavity. With a screwdriver blade, touch the lugs of the volume pot. The earthed end will remain silent, but there would normally be a buzz from the other two lugs, if the pot is set to max. If there no buzz at all, check the wiring between the pot and the jack socket.
If you can identify the wire from the pick-up to the circuit, touching a screwdriver blade to each p/u connection should provoke a buzz. If there's nothing, check the control wiring. If there is a buzz, the p/u may be faulty.
There's the simple, non-tech way of seeing where to look. If you're a solderer, it's also easy enough to undo the p/u wires and take them straight to the output jack; just make a note of where they were before changing anything. Good luck with the hunt; keep us posted as to progress, please..?