Yes, Your LT1 PCM does control your Fuel Pump and your ignition if it is wired to do so. Some PCM wiring does not while others do. I would suggest that you get ahold of a scan tool for OBD1 and scan your PCM while turning it over. You can likely get an indication of what is going on. It could be something as simple as a fuse (I have three that control the PCM) or a ground for the PCM let go. Since you don't get your Fuel Pump activated while the switch is on but prior to the switch in the start position, these are the most likely things that can happen on your LT1.
Jerome