So I did the movie fix for the DDERR GENERIC error, and I also downloaded the Last Resort mod, but the same thing happens. I tried adjusting the compatibility settings too, but no matter what, I start up the game and then it minimizes after the Sierra logo intro and if I try to pull it back up, it pops up for a split second, then minimizes again. Sometimes, depending on compatibility setting, I will get a string.dat error. Please help.

I am running this on:
Windows 7 Professional (64-bit)
Intel Core i7 @ 2.60GHz
Nvidia Quadro K1000M
8GB RAM

Try to install this - http://www.microsoft.com/en-us/download/details.aspx?id=8109

I extracted the contents to a folder on the desktop, ran the setup file, the Last Resort mod works now, though the menus are really flickery

Actually, nevermind, now it stopped working on the mod.

Try dgVoodoo, it's what I use for most old games like this and it works flawlessly, but maybe your problems lie elsewhere. You'll basically need to copy paste 3 of the included files in the main SWAT 3 directory, dgVoodooSetup.exe, D3Dlmm.dll and DDraw.dll then run dgVoodooSetup.exe, choose the desired settings (for D3D in this case) and run the game as always. If it doesn't work delete the files, it doesn't alter anything so it won't cause you problems with anything else you try. Just try it on a cleaned installation first to ensure nothing else messes it up either since you've already tried all those other things that failed to fix it for you.

http://dege.freeweb.hu/