Try creating a shortcut to the engine executable with -log and -dx12 appended to the command line. That way you’ll at least get a peek at the output details while it starts and I’ve found dx12 more stable than dx11 on my systems.
I had a somewhat similar issue on my first run of 4.20, upon initiating the project launcher for that version my computer just immediately restarted. Hasn’t happened since, but I’ve never had that issue with any of the prior versions so it’s safe to say something might not be right with this version. I hope you’re able to find a solution, or Epic will be able to resolve it.