Actually I have two broken power door locks. The driver’s door power lock does not work at all. You hit the little button to lock or unlock and nothing happens. The driver’s side back door is broken too, but in another sort of way. It works when you operate the remote to lock or unlock, but whenever it locks, it makes this awful screeching sound that sounds like fingernails on a chalkboard, but louder and more annoying. Any suggestions as to what might be wrong or where to get spare parts? I am a relative novice when it comes to cars, but I’m pretty handy with tools. I do change my own oil 
Your first step should be to squirt in some WD-40 or other lubricant into the lock post. See if that improves matters. If there is no improvement you will have to remove the door panel to investigate the trouble. This is not hard to do. Once it’s off you can see exactly what is malfunctioning.
The broken door locks must be a quirk with this year Neon. I have the same trouble–just different doors. Haven’t fixed it yet–I just don’t hit “lock” on my keychain until I make sure no one is around. I have made quite a few people jump when making the car “screech” behind them.
I too have a dodge neon, 2000 ES and it has had two broken door solenoids that have gone bye bye. one on the passenger door and one on the driver side rear. Both of these door had the same sound as you have described. These happend about a year apart. Looks like thay have a problem with locks.
Did replacing the solenoid fix the problem? How hard is this to do?