cody2209: I have tried multiple solutions and none of them have worked
I had also tried all the suggested fixes multiple times and had no luck until last night, when I stumbled across an obscure forum post that led me to add "-window" as a command line argument (which launches the game in windowed mode). This prompted an error message telling me that the game required 16-bit color mode, so I went and enabled that as well, and it's been running fine ever since.
To note, I'm also running SWAT 3 with the usual compatibility options (administrator, XP service pack 2) and I've also done the xvid codec replacement movies and -nointro command line argument. I went ahead and checked "disable fullscreen optimizations" as well just in case, since I'm having to run in windowed anyway.