Problem with keyless entry (2008 Prius)

I've been having a problem with my Prius which I can't figure out. I've searched around for someone else with the same problem with no luck. So here it goes.

About a year ago the back doors to my Prius stopped working. First one side and then about a month later the other. Basically when I would lock and unlock the doors the back doors did not respond. So I would have to manually lock and unlock them. Not a huge deal since I don't use them too much. Now however when I touch the drivers door to open it (with the key in my pocket) the lights flash on and off, I hear a clicking sound coming from someplace under the dash, and the door will not unlock itself. So I have to use the physical key to unlock the door. The ignition button still works fine once I get in.

Any ideas what could be causing this? I did try lubricating the rear door assemblies but that did not work. I also tried replacing the batteries in both remotes which had no effect.

 

I replaced the 12v battery in 2012 at around 122k. The car has 152k on it now. If I press the button to unlock and lock the doors the drivers door locks but then stays in the lock position and will not unlock again (unless you manually move it with either your hand or the physical key). The back doors will neither lock or unlock when I press the button, you can control those manually however. The front passenger door still works like a charm.

 

I believe your comment regarding the "door lock solenoids" is just what I needed. Using that term I found this article:

Fixed: Door Lock Actuator in Gen II Prius | PriusChat

which seems to be what I need. Thank you.