I tried to install Demon Stone on my PC several days ago, but it wouldn't work properly. The install gets to 99% done, then pops up with an error message that says

Componenent: Default Compenent
File Group: Default File Group
File: D:\data3.cab
Error: Data Error (cyclic reduncancy check)

The DVD is in perfect condition and I far exceed all minimum system specs. The official forum for this game on the Atari website has yielded no answers at all, nor has the Atari technical support! Honestly I'm pretty pissed off at Atari right now. Does anyone have any idea how to get this game to install?

Well, despite the DVD looking fine, as you say, a CRC error pretty much always means there's a problem with the file(s) in question. "Data error" is even more obvious.

Try copying that file off the DVD to your hard drive. If that also fails, it's pretty much proof that the file is bad, and you'll have to get the game replaced.