The lock/unlock switches on both drivers' and passenger's side doors have stopped working. I replaced the battery in the remote and the remote seems to work fine- I know the battery is old ( the original unit from 2006). Could this problem be another symptom of the car battery needing replacement? Anything else to check before I spend the $$ on the new battery?

 

check the voltage on the battery
you can always take the battery to a local auto parts store and have them test it.

oh, and avoid Optima batteries.