sounds like a bad connection at the battery, solenoid, or a bad ground, replace both batt cables, you can have some one try to start engine while you check to see if one cable is real hot, if so bad cable or connection
The small wire that connects to the sol is trouble on many of those that's why the new starter comes with the wire connected and a crimp connector which you should use. check this 1st. good luck
On some cars of that vintage there was a pair of contacts under a little curved cover on the starter. If the battery gets old, the car will start, but the current draw will heat up the contacts and they fall off. I silver soldered one back on. Most folks buy a rebuilt and toast that one too because they don't change the battery.
oldbugger hit the nail on the head corrosion on the terminal at the starter i replaced this wire 8 mos. ago i guess china has struck again. this conection was heat shrink wrapped from provider so a $.50 part cost me $170.00 and a day and a 1/2 in time but i can get the starter out in 5 mins. now thanks now back to the c---y camaro resto.