If you are 200% positive that you tried the pairing procedure the right way (I myself find the procedure totally retarded, being used to the E60 and later procedure):

1 Try forcing the ULF to go in pairing mode with navcoder or similar software.
or
2 Unplug the big black connector on the ULF module and the maroon&blue connectors of your MK3 unit (since you suspect the MK3 is acting up), for a couple of minutes and then plug them back in.

By "I'm unable to get the car to enter pairing mode at all" you mean that you don't even get the "Bluetooth Pairing" message? Or you get the message but the phone and the ULF don't sync?