There should be 3 wires on the starter solenoid.
The big battery cable from the battery on the big stud. With another wire also on the same stud. Probably red and around 10 or 12 gauge.
Then there is the purple wire on the small stud closest to the engine block. The purple wire should go directly to the big through the firewall plug between the steering column and the drivers side fender. With a test light, volt meter, power probe or whatever you have. Test again at the battery with someone turning the key to start. If still nothing on the purple wire try the purple wire at the firewall. If nothing there you have 2 choices.
Crawl under the steering column, probably removing the AC cross over ducting to have any access, and look for the purple wire on the ignition switch. Test for voltage there with the key on the start position.
Or
Remove the bolt from the middle of the massive through the firewall plug. 1981 should be 10 mm socket. It could be 3/8 or 7/16 though. GM used a black sticky goo inside this plug. It will look a mess. You should see any signs of arcing if that happened. It is also a good idea to use a small finger nail file to clean all of the connections on both sides of the plug.
Another thought is about the other wire on the big stud of the starter solenoid. That red wire goes to the diamond shaped Buss bar near the brake booster up high on the firewall. Power to the ignition switch comes from this location. There should be several fusible links on wires there. Verify all the wires going to and coming from that location have continuity. Also, verify the nuts are tight. I had one that cracked and was causing everything to turn off when I turned to start. Which brings up that.
Are the gauges coming alive along with idiot lights when you turn the key on? Are they still on after you tried to start?
Then the most obvious. Is the battery hooked up, fully charged and load tested to be good?