I don't think the game has a CD key that needs to be typed in. I have the Xbox version, but have not seen mention of such a key in the forum for the PC version.
What is the error message? The copy protection may just not be finding the DVD. Try a different optical drive, if available; I've seen the lowest drive letter one recommended, with comments that Securom can be picky if there are multiple optical drives.
You could also try uninstalling the game, rebooting and reinstalling. Maybe there was a conflict with one of the other games trying to install at the same time. Alternately, I believe Securom has a utility to remove / update / reinstall their drivers.
First Aid : when Div2 does not start or crashes