I know that this doesn't fix your issue, but may provide you a workaround. I still need to create a log and submit my issue, as it is similar.
I have (LGX) GC550 | AVerMedia. I updated the driver and to Rec Central 4. I've been out of streaming for several months, and thought it a good idea to start fresh and up to date. That said, I am also running 20.1.3 64 bit. I too get the blank screen now. I found an oddity where if I leave the video capture enabled (I do not use a web cam) when I shut down, it comes up blank at my next startup. I created a duplicate Video Capture, and this is how I get around it... for now:
When I start up the next time, I disable the previous one that was enabled, and then enable the one that was disabled. I alternate. If I have only one, I might have to start Rec Central, let it run for a few minutes, close it down and then run OBS. By doing it this way, with the two capture sources, I have given myself a 100% guarantee that it'll work... albeit in an awkward manner.
Anyone from OBS reading this can contact me directly with any specific steps to capture this correctly in a log, or otherwise. Until I can sit down and better articulate this with an error log, I thought to stop by here and provide a workaround for Wyrlwind. I actually stopped by because I heard that there was an update and was hoping to read something about this very thing.