My switch on the drivers side, would fail to function during the summer, when the interior temp of the cabin got real high. I put my thumb dead center on the switch and pressed straight down (no rocking of the switch). I actually heard it click into place. Apparently it was never fully seated from the factory. Might want to give it a try??
I work at a JY. I noticed I get a lot of calls on 94-04 Mustang door latches. Some times the latches them selves go bad. They also have a lock actuator that pops up and pulls down when locking and unlocking the doors. Check those out. The actuators were notourious on the fox bodies.
FWIW, a little lubrication at the joints of rods and at the locking solenoid will help a lot. It's a pain to take the interior panel off, peel back the plastic and get access to the whole mechanism but you will find that light corrosion builds up and stiffens up everything. Use lithium (white) grease or WD-40 or PB Blaster followed by WD-40. Should help a lot.
If the passenger side locks and the driver's side doesn't, it's the door lock solenoid. I've replaced either 3 or 4 of these (I've lost count), one of them on my Taurus SHO (RIP). To replace the door lock solenoid you've got to remove the door panel and drill out the rivet that holds the solenoid in place. It's more tedious than it is hard.
On a side note, there's a rubber sheath that protects the solenoid mechanism from water and dirt. The one on the SHO was rotted almost completely away, so that when it rained and then later froze, the door lock became inoperable. A new lock, with a new rubber sheath, cured that issue right away.
If neither of the door locks work, it's probably the switch. They tend to get corroded and fail. You might brush it lightly with some muriatic acid and wash that off immediately (believe it or not it worked for me on the SHO) or get some color TV tuner cleaner at Radio Shack and try that (mixed results). Or break down and buy a new one for about $50.