If you have upgraded to eLicenser Control Center 6.12 on Windows, either by installing Dorico 3.5.10 or by installing eLCC 6.12 directly, you might be falling over an acknowledged issue on Windows that causes Dorico to hang at the splash screen on some systems. The work-round for now is to uninstall eLCC 6.12 and install 6.11. There is no need to downgrade Dorico - 3.5.10 works just fine with eLCC 6.11.
There is more on this issue here (click), including download links for eLCC 6.11.
My apologies if this is nothing to do with you issue - it’s Ulf you need to be listening to really. I just want to mention this here in case there is an easy fix for your problems.