While many problems could cause the power door locks to not respond when hitting the button, a broken Door Lock Actuator is a very common culprit, and is a very common part failure on Fox Body Mustangs, particularly older models. The part resides in the lower portion of both doors, making its replacement seem a little intimidating. However, as Bill demonstrates in this video, the install really isn't anything to worry about, and he provides step-by-step instructions for the whole process.
As long as the bracket that attaches the Door Lock Actuator to the door is in good shape, the replacement process is fairly straightforward. It will only take an hour or so and require simple hand tools, though it will take a little time to remove the door panel to access the actuator, then remove the old actuator and install the new one in a fairly tight space.
Check out the video as Bill guides you through the process, so you can fix up your Fox Body to lock and unlock again!