The first thing to try is to reboot, wait a few minutes for Windows to finish its background loading, and then try starting the game again.
Rebooting seems to solve a number of mysterious problems.
When I start the game, the first thing it does is display a window asking about my screen resolution. When I accept what it detected, I get a black screen for maybe a minute while my hard drive light flashes. Eventually I hear the game and it shows the Shadow Tor promo and loads the Main Menu.
Anyway, try rebooting first. If that doesn't work, try right-clicking the game shortcut and Running as administrator.
If that doesn't work, we'll have to check your specs, and if you meet the specs, you may need to add the game exe to your antivirus' exclusions list.
Maybe Draclvr will have more ideas.
These are the system requirements:
(listed at http://darklingroom.co.uk/darkfallgames/darkfallghostvigil/
Launch OS: Windows 7, 8, 10
Processor: 3.0 Ghz (intel Core i3 or equivalent or higher)
Memory: 8 GB RAM
Graphics: 1 GB nVidia Geforce GT460 or equivalent
DirectX: Version 9.0c Upwards
Storage: 6 GB available space - TBC
Sound Card: DirectX Compatible Audio
Launch Language: English
Mouse Controlled. Keyboard Control. Controller Control Compatible.
Additional Notes: Wide Screen monitor required.