Prerequisites for a successful PATS prove-out:

1) PCM is properly receiving power. Check PCM power relay and related fuses. Verify that MIL illuminates during bulb prove-out.

2) Instrument cluster is properly receiving power. Check all related fuses.

3) Check the connector on the transceiver ring around the ignition cylinder. The ring is an antenna that excites the RFID chip inside the PATS key and reads the response.

Your 2001 has built-in diagnostics that include certain PATS functions. SEARCH (or google it) phrase "+HEC +Dealer +Test +Mode" to dig it up. Post any DTCs that are displayed.