If it never chirps, the DUH! solution is the horn is not working.
Assuming that is not the case, the only thing I can think of is that either you have a different BCM computer or you are not following the EXACT procedure given.
1. Set the parking brake.
2. Turn the ignition switch to RUN with the engine off.
3. Turn the headlamp control from off to parking lamps four times within three seconds.
Maybe the parking brake isn't being recognized? You should see the light on the dash when in run mode. Run is not accessory. It is RUN. Parking lamps are not headlamps.
Even if you have the wrong TPMS sensors you should still be able to get into the relearn mode. Again, though, if all 4 sensors failed at the same time then it is the receiver and I'm not sure if you would start relearn with a bad receiver.