Yep. The synch code means that one or both of the door latch mechanisms have faults and are not both locking and/or seeing "door safe" when the door is closed. Do the windows fail to drop when either inside or outside door handle is used?
It could still be an immobilizer or wiring issue, but the door latches are the obvious answer.
I would also remove the aftermarket keyless entry until the problem is solved because it very well could be contributing or causing the problem. If you want to keep using an aftermarket keyless entry, thoroughly test the unit you have or just replace it. The $13 unit I use has excellent range and has worked flawlessly for years, so a decent one is not expensive.
