Finding CD keys from steam?

I bought company of heroes on steam a few days ago, but whenever i try to start it through steam - it wont run. i followed all the support steps steam has online but none of them worked... when i went into program files/steam/steamapps/common/comapny of heroes and ran the company of heroes application itself, the game would start up to the main menu but then require that i give a product key to play it. is there a way to find a product keyfor something you've bought on steam? (i thought i heard something about how the registry might work) I have vista btw... any help would be great