If you had another DirectX game to try that would help narrow down the problem. A system issue (outdated or corrupt drivers, bad RAM, etc) should effect all programs that make heavy use of system resources. If only DD has problems, then the source would have to be in the game itself (which the file verification procedure may identify) or a conflict between it and a driver or background program.
The graphics benchmark
3DMark has a demo which stresses graphics more than most games do. It has been awhile since I've use the program, though, and I don't recall if you can loop the demo in the free version. If you have a high speed internet connection and can handle the 178MB to 580MB download (depending on version), check out the system requirements first (for example 3DMark03 supports Win9x, but 3DMark05 and 06 require at least XP).
There may be other, smaller graphics benchmarks that would work just as well for this purpose.
Anyway, LMK how the other troubleshooting stuff goes.