Just bought a used 2001 4.4i, and the PDC did not work. Oh well, I guess I'll have to get used to the fact that it has a solid beep for a few seconds when I throw it in reverse. But after a few weeks, decided to take it to the dealer and see if it could be fixed. The dealer charged $170 for diagnostics, and they said the "rear PDC harness" was damaged from the exhaust pipe, and that it would cost $750 to fix that - however, there was no guarantee that it would completely fix the PDC system. I'm not going to spend that kind of money, and perhaps not have it fixed!
So I wondered, "what is the rear PDC harness?". Without taking off the rear bumper, I could see that there was a wire near the right rear exhaust pipe that was heat damaged. I guess the dealership calls a wire a "harness". With some spare copper wire (narrow guage) and some electricians tape, I fixed the burnt out wire, and secured the wiring higher up into the bumper so it wouldn't fall down again against the tail pipe. So now the PDC system....still did not work - bummer. Maybe one of the sensors is shot?
With the key in the ignition and the car in park, I hit the PDC button (steady beep stays on for a few seconds) and checked all the sensors (as one of the other posts described) by putting my hand against them and closely listening for some clicking noises. It turns out the left rear sensor is not working! So, I figure I need a new sensor. But I decided to check to see if it was just a wiring problem again. Again, from under the bumper, without taking the bumper off, I could feel that the wiring was loose. By pushing the connection in tightly, the sensor worked!! However, there was no way to keep it tight. So, I pried off the sensor cover with a screw driver, and then the sensor came off through the back. I don't know if that was the wrong way to remove the sensor, but I needed access to the wiring connection. I could see that there was a small piece of rubber in the connector that was preventing it from making a tight fit with the sensor. I removed the rubber piece with a screw driver, and now the sensor made a tight fit with the connection. I put the sensor back in, and had to epoxy the sensor cover on because one of the clips broke off.

Now the PDC system works, and it cost me $0 (except for $170 diagnostic from the dealer)!

I just thought someone else might want to read about my story if they have a similar problem.