Given the year and model, it's almost certainly the relay. Usually, the
relay contacts burn from arcing, and even though you hear the click,
there's no electrical contact.
There's a door unlock and a door lock relay located in the fuse and relay
box behind the switch panel on the left side of the dash. They're
identical, and the problem could be in either one. I can usually pull the
relays out using an angled pair of pliers. Feel on the relays with your
fingers to see which ones are clicking when the switch is moved one way or
the other. Then pull one out, go to your local dealer and purchase one.
Put it in, and recheck the locks. If they still don't work, swap the
other lock/unlock relay.
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