Not sure what caused the issue, I did have a PlayStation controller plugged in to my PC when the problem occurred so I don't know if maybe that messed with something although unplugging it and restarting the PC didn't resolve anything. If it happens again I would maybe be able to narrow down what caused the issue further.
The fix was just to uninstall the game and remove the Dark Omen folder and any mentions of Dark Omen in regedit (I think I may have missed some entries which made this not work the first time I tried it) and then install the game again. That is one of the fixes mentioned in the fix guide. I tried a bunch of other things to try and fix this issue without an uninstall but the uninstall is the only thing that worked.
If you have this issue and you have to uninstall the game and you don't want to lose your current progress, just copy the SaveGame folder located in the Dark Omen folder and paste in your saved games with the fresh install.