Let me guess: Carb AND a non-stock, non-computer-controlled distributor?
If that's the case, the distributor is not communicating with the ECM, the ECM never receives the RPM signal that tells it the engine is cranking. Therefore, it never turns on the fuel pump relay.
Depending on how screwed-up the wiring is after gutting the fuel injection and stock distributor, that could be the reason it doesn't prime, either. Priming doesn't require a cranking/RPM signal, so lack of priming is likely a second failure, but maybe related to the carb/ignition conversion.
But even vehicles that haven't been tampered with can have fuel pump relay issues, which might be a defective ECM, defective wiring between ECM and pump relay, or a failed relay.