Fuel injectors won't open

Wow! an '82. Nifty. Yes, it could be a grounding problem. The older systems used injectors that draw a lot of current. Especially check grounding between the fuel 'computer' box and the engine. Physically/visually check terminals or use a light bulb tester. A volt-ohmmeter is not reliable when checking high current circuits because it doesn't demand high current flow.

I saw the exact type of thing on an older BMW not long ago.

This is a common problem first try carefully remove the retainer clip wire that holds the plug on use a volt ohm meter plug them in plug set for 12v dc turn engine over to see if your getting pulse from ecu if not check fuel injection relay check all your your relays try using dielectric grease and lightly coat all pins push up and down to allow good contact with all pins if you are getting good signal bad injectors