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Is there any documentation available on removing or repairing antennas on a 82 model.
Shop manual is probably the best source. Can you hear the motor running? If that's the case, than replacing the weed eater cable will probably work. It can get more complicated after that.
If the car has been fondled by bubba, it could be anything from mechanical to electrical including connections to the radio, the power antenna relay, etc. So you need to do some troubleshooting.
I've gotten away at dropping the left muffler to access the antenna. Get a test light and determine if you've got power to the unit. Isolate if its in the unit or up the line. I'll assume you've checked the fuse.
The 82 Corvette Shop Manual has a nice troubleshooting guide along with circuit schematic. Others may have it scanned and can post. If not drop me a note and I'll scan over the weekend. Also shows location of the relay (console).
Unbolt the exhaust system at the rear of the catalytic converter (4 Bolts) and the whole rear y-pipe and muffler assy will basicaly fall out giving you plenty of access under there. You will need to unscrew the bezel from the top. The wiring harness unplugs from inside the passenger compartment. Pull the carpet away over the rear drivers side wheel well area to find the harness plug and the rubber grommet that you will need to push out to the rear of the car to get the wires disconnected. You should be able to take it from there.