After I exit the game, the program HotlineGL.exe still shows as running on the Windows task manager. If I try to run the game again while this remains in effect, the game will not start up, though according to the task manager this does add another instance of that program running. I have to shut the program down manually from the task manager. Possibly this is related to the fact that the only way I can run the game properly is by setting it to run in compatibility mode. I'm running this on Windows XP with Service Pack 3.

Try running the game explicitly as Administrator by right-clicking the file you use to start it and selecting Run as ..