So the door ajar chime stays on? Check all the switches that would power that relay. Not sure if these cars use a simple relay system though, power through the switches could go to a module first then to a relay. How do all the doors feel when you close them? Do they close tightly, i.e do all the latches engage with affirmation? Could be that one of the latches isn't "grabbing" enough to open the switches, door doesn't stay in far enough to depress the switch far enough. Does the door ajar light in the dash also stay on? The fact that the key fob doesn't do what it's supposed to indicates to me a bad BCM or IPDM. There shouldn't be THAT much wear in all the moving parts of the doors for it to be that, same with an ignition switch. The BCM may not be powering the lock actuators to lock the doors because it's seeing an open door, or what it thinks is an open door, and that could be why it will unlock but not lock. The BCM may refuse to lock doors if it sees one or more are open. Since the automatic interior lights (light in hatch/trunk, cabin lights) will stay on if there is an apparent door still open, test this by making sure everything's closed and watching the trunk/hatch and interior lights, they should go off after whatever period of time they're supposed to stay on for after all doors are closed. Something like 10 seconds maybe. The two mentioned problems are probably linked. I wouldn't rule out a bad module, they do randomly go sometimes. But don't do that first, do proper diagnostics like I mentioned to pinpoint the causes.