Check for a lost neutral, Even though your non contact voltage detector is not the right tool for this, its giving you a clue that some sort of voltage is present. Get a meter that actually reads voltage. Since it sounds like you may be sharing a neutral between these to circuits, dont plug anything in them. First read from hot to neutral, if you have nothing, then try reading between hot and ground, assuming you have a ground in the circuit. If you have a ground and read 120 volts or close to it, with in a couple of volts, then you have lost a neutral. If you dont have a ground, then use a extension cord plugged into a good circuit, and use the neutral in this to read across the hot in the dead receptacle. If you read 120 volts it will confirm you lost a neutral.
Now you will have to find where you lost it at. I would start in the panel. If you are not comfortable with this, please call a professional. If your connection seems tight on the buss, then start removing receptacles to find it. It could also be in a j-box in the basement somewhere, depending how it is wired. Main thing is turn the circuits off and if you are not sure, hire a professional.