92 F-body will not Start

Check fuses first.
I would bench test the starter. Some freshly rebuilt ones crap out in no time.
If starter checks out good, check for voltage at the little wire on the starter (disconnect it from the starter before testing) while an assistant turns the key to start. If no (or low) volts, check the ignition switch under the dash.

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.