I'm experiencing similar issues. I just had the MOSFETS on the kessy repaired and it seems to have woken up my push button lock on all doors but the rear doors do not lock (even though pressing the button works) and do not unlock the doors/disable the alarm when I touch the handle. This seems to work fine from both front doors. I also installed keyless start and that is working fine with the key in my pocket. I also seem to still be experiencing battery drain even after the MOSFET replacement. I saw a suggestion to pull the fuses for the doors to 'reset' them. I'm going to give that a shot and hopefully that helps with at least getting the doors to lock so I can feel better about leaving my vehicle unattended in parking lots while I'm out and about.
Edit: I have a 2004 V8
Edit: I have a 2004 V8