Sounds like the classic corroded positive battery cable problem. This happens a lot. Especially if you have the factory AC Delco battery. Corrosion gets inside the cable due to a leak in the positive treminal of the battery. But the corrosionin the cable happens with other batteries as well. The only reliable way to fix it is by replacing the cable.

 

Just fixed a simular problem with my 93 S. Look for "93 S won't crank" in the forum. The solution to my problem was to remove, and insulate the analyzer connector located on the panel, under the dash by the driver's door. Also good tips on chasing the "switched voltage" for the starter solenoid, which enabled me to find the problem. Hope this helps!