Just a few questions to get a better handle on the fault (because I think there probably is one, like Greg said), and my thoughts on a likely cause...
Does your LP have one tone knob or two?
If two, do they both have the same effect on volume?
If only one affects volume, does it do it to both pickups?
Does the tone pot in question actually affect tone?
Try measuring the resistance across the capacitor, because if the capacitor has shorted internally (which is quite unusual), or it has a short across it, that would explain your fault...