Is it possible that the instrument panel itself failed? Is it common? The 3 lights (ABS, Pads, Parking) that come up actually lit when the key is at ON, and they shut off when the engine starts, then they lit again approx 1 sec after ignition.
I also noticed that when I start moving the car with the parking brake activated (for real), the beeper does not sound anymore. I therefore suspect that this is simply due to the instrument thinking that the car does not move.
Do you know if the speed sensor cable is routed below the radio, and then near the shifter assembly? Is the sensor in the differential?