Hmm, I really don't know what it is, but if I'd have to take a guess or two... Maybe your CD/DVD reader doesn't read correctly. Maybe the last CD - assuming it happens with that one - is damaged and then certain files can't be found.

Hmm, maybe an evil spirit is haunting your PC and influencing it for some reason wanting to prevent you from playing this game?

I dunno... but it sounds like a faulty copy of some sort. Maybe you could try out the Apothecary or something, or the Hardware forum.

Hey, I just quickly found the following (http://planetcoh.gamespy.com/faq/index.php?category=1):
1.5.20 I put Company of Heroes in my CD drive, and nothing loads. (0 comments)

If your computer isn't picking up Company of Heroes in your drive, try another CD drive. Alternatively, check to ensure that you are putting a CD version into the CD drive. If you purchased a DVD version, it will only work in a DVD drive.

Might be of some use to you.