I tried to run this years after it was released now in 2012 and ran into a few problems on my Win7x64 machine with a Radeon HD 5850 and current drivers. First it crashed on the DiRT 2 logo screen, then after getting farther I hit problems of freezing up after playing for ~30 seconds.
It works for me now after taking two steps:
1) Install a current version of Blue Ripple Rapture 3D. The demo came with version 2.3.26, I just installed version 2.4.11.
2) Edit My Documents\My Games\DiRT2 Demo\hardwaresettings\hardware_settings_config.xml and change directx forcedx9 to "true".