I have a Dell ST2320L_HDMI monitor and a ATI Radeon HD 4600 Series. The PC itself is a Dell Inspiron 530S.
I'm running Windows 7 Home Premium. The Device Manager says my current driver for the video card is up to date.
Have you examined the Event Viewer to see what program crashed, or what Windows has to say about the crash? Is it the same video (will it run fine with a different video)? Is it the same player (does it crash with Windows Media Player, but run fine with VLC)? How long has this been happening? Were there any changes to the system before this started happening?
In short, see what Windows has to tell you about why this is happening.