This is an extremely common problem in these cars. The signal wire going to the starter gets old and starts to have resistance, not allowing full power to go to the starter trigger solenoid, therefore it can pull the solenoid so far, but not far enough to get the contacts to touch for the starter to turn. That is why you hear a single click. It is an easy fix, you just have to wire a relay into it. Wire it as such using a wire as big or bigger than the original blue trigger wire. Use these crimp on connectors, they slide strait onto the relay spades and the starter spade. With this circuit, you can use the weak blue signal to trigger full battery voltage to the starter.
RadioShack.com - Cables, Parts & Connectors: Connectors & connectivity: Crimp connectors & terminals: Crimp-On Quick Disconnects (6-Pack)
^ those come with male and female connectors, but you only need the female ones. You will need 4 female connectors so you would have yo buy two packs. Hope this helps you. If you want proof that this will work, hook a jumper wire from the battery positive terminal strait to where the blue trigger wire connects on the starter, and watch it crank everytime.