Mazda5 Door Lock Issues

Having two issues with the door locks.

One: the remote stopped working, so I tried reprogramming it (brand new battery) using the "open drivers door, cycle ignition 3x, open drivers door 3x" method, but at the point where the locks are supposed to cycle on their own, they don't.

Two: the lock switch on the door doesn't work without the ignition being on. I press it but nothing happens. The doors do lock when I use the key in the outside lock. I don't recall what the behavior was like before the remote stopped working, so I have no idea if it's related.

Any ideas about either issue?
I don't have a "key not detected" message though. I don't think I even have that function. I have a chip in the key, not some kind of RFID/proximity sensor.
What if your door lock actuator is going bad? Not enough power from the battery to actuate, but enough from the generator?