HTWingNut: I can't launch it either. Windows 10, i7-5820K, GTX 980 Ti, latest drivers. No compatibility mode will launch. I just get the little SWAT 4 window and it sits there.
If the game has created the ini files you can try forcing the resolution and maybe force windowed mode.
http://pcgamingwiki.com/wiki/SWAT_4 There are some resolutions or aspect ratios that the game may not support. Such as Ultra wide or 4K.
http://www.widescreengaming.net/wiki/SWAT_4 After making changes to the ini file you have to set it as read only. And just OK the pop up error message when you run the game.
The problem this solution might solve SWAT4 always seem to try to detect the resolution every time you start the game and resets the resolution. It also overwrites any changes you make to the ini file on every start and exit of game. If it can't get the resolution or somehow at least 640x480 can't be set (or was it 80x600?), I think it starts acting dumb.
You may want to change the main menu resolution settings in the ini file as well (if I recall correctly).
If anyone wants it, or does not have the SWAT4.INI files, I can dump my ini files when I get home later.