OK, if you have access to an ohm meter, you should be able to figure this out. If you don't have one, get one, they can be had fairly cheap, and a cheap one will do just fine, you can get one for under $20 at radio shack or similar places.
OK, so, looking at the
schematic for the 4001C64, we see that the treble tone pot goes from the 0.047uF cap C2 to ground. When it is turned all the way down, it will be shorting the cap to ground. It's supposed to do this, so, if it's killing all the signal from the pickup, we can assume the signal from the pickup is somehow getting directly to the pot and not going through the cap (well, if the cap is shorted internally, it would be going through the cap, just not the right way).
So, set the selector switch so that the bass pickup is selected. This will isolate the treble pickup circuit to just the pickup, tone cap and pot. Now, take your ohm meter and measure across the pot. You should get a reading that varies as you turn the knob from nearly zero to somewhere around 330k ohms. If so, the pot is fine, which I'm pretty sure is the case because from what you've described, it doesn't sound bad. Leave the pot set at the 330k setting.
Next measure across the cap (you can do this first actually, it's just that understanding the measurement might be easier if you do the pot first). Here, you should be measuring the resistance through the pot and the pickup (through the ground connection) so you should see a value of 330k plus the pickup resistance, which is something like 12k. If you see something less than the 330k you left the pot at, especially if it's close to zero, you can assume that either the cap is shorted internally or something else is shorting the cap somewhere.
It's unlikely that the cap went bad internally, they're pretty robust parts. But, it's possible that somehow, bending the wires caused something to short inside. And that's pretty much how the cap would fail, either open or short, the cap is just a roll of 2 sheets of thin foil separated by a layer of thin plastic with one lead connected to each sheet of foil. They're pretty simple, not much to go wrong.
You can also unsolder one end of the cap and measure it all by itself. This should look like an open circuit, just like you weren't touching anything with the meter leads. But of course, this requires more soldering work...
