My power locks on the '01 have been on the fritz also. It is pretty common for door speakers to die on the newer XJ's due to busted wires near the hinge. I assume the same thing is happening there. Do you power locks lock when you use the passenger side button? Do they work when you use the remote? Do you hear a click?
-2001 XJ Limited, 4.0L, NP231 w/ SYE, AW4, 4.5" Lift, 32" tires, 4.56's
-1987 XJ Pioneer, 4.0L, NP231 w/ SYE, NV3550, 4.5" lift, 4.10's, D44 rear