Hi all, my daughter has an '88 mustang with the 4 cyl. in it. The battery is fully charged, but sometimes it just clicks once and that's it. I had this same problem years ago on an '84 mustang ghia with a 255ci. in it. Seems to me that it was the voltage regulator mounted on the fender well that was the problem then, but can't remember for sure. Any clues?
Before you get all wound up changing parts, make sure that the battery is fully charged. Next, use booster cables, or something suitable to substitute the existing battery leads. The problem could be as simple as that.
A rusted connection at the starter could also be the culprit. If the starter on that car has a solenoid on it, take a screwdriver and jump the battery lead at the solenoid to the power lead for the electric motor. If it is the non-solenoid type,you will need someone to be holding the key in the start position while you BRIEFLY short out the lead at the starter. This will NOT make the bendix kick out on the first type of starter, but WILL on the second. What this does is uses max battery power to "burn" through the rust.