I've got you covered, I installed DiRT 3 the other day! (Just to let you know, it's AMAZING!)
Anyway, Games for Windows Live would be good to install first, and also the .XNA Framework (trust me, it does help with certain game installers, no idea in how it does but oh well).
Also, try (in My Computer where it shows HDDs and disc drives), right click the DVD drive with the disc in, and select "explore". Then find the setup file, and right click, RUN AS ADMINISTRATOR. It's a large game (11.6GB) and it took me about an hour to install. Just sit it out and wait if it does get working.
Stupidly, Codemasters made it say "Configuring DiRT 3", instead of "Installing DiRT 3". It's confusing I know. But when it says configuring, it means installing.
It's a good game if you also play Race Driver GRID