Power locks malfunction in multiple ways intermittently on 2003 Chevrolet Malibu

My power locks no longer lock when I start my ignition or unlock when I turn the car off. They also won't unlock with the power lock switch. When I get out of the car and try to lock the doors with the power locks, they either don't respond at all or, after pushing them a dozen times or more, they unlock rather than locking. Any ideas?

Asked by for the 2003 Chevrolet Malibu
posss fob issue try another key fob 1st or change battery in fob
I actually don't have keyless entry. So, I'm clueless. :(