Had the same problem a couple years ago on same 396T, for others this is the same setup on a 396XT. Opened it up and unless you can find someone that can do soldering on small circuits with a fine tip soldering and a microscope, forget trying to resolder. Way too small of an area.
I found if I pushed the knob to one side it would work a bit, most times it would go opposite direction I wanted.
Sent it to uniden and had it back in 3 weeks, but what they replaced was a lot.
Everything seen on the outside replaced, case, keypad,glass, antenna connector, rubber along the bottom, new knob. Essentially a new radio short of the circuit board. I only mentioned the knob problem to them, the keypad center was a little worn and the rubber was worn, other than that all was good.
Charge was 59.50 + 10 to send it in.
http://www.uniden.com/page/productrepair