You didn't say anything about whether you could hear the solenoid click when you tried to turn it over. In my experience, I haven't had any problems with the HEI coil.
You can always buy a remote starter (basically two connections with a push switch in between, they are usually pretty cheap). The remote starter connects to the input and output of the solenoid as a bypass, and if it turns over you know the solenoid is bad. Solenoid is usually the bad player in the GM starters, even with "new" starters. Hopefully you've got a good warranty on that starter.
I had the solenoid go bad in my 77 Chevy Impala, 84 Firebird, 86 Z28, etc. Same basic design in all of them, it gets subjected to so much heat next to the exhaust, that its not uncommon to see them fail over time. Summit Racing sells a remote solenoid kit just for GM vehicles for that very reason.
Saturday, August 17th, 2019 AT 4:58 PM