That's an easy one: because EF is not asking the key, Steam and CoH are and you are running the wrong game most likely. Unless you can submit an screenshot to prove this wrong. If you want to know the serials you just need to right click on the games' entry on the library and select the option to view the cd keys from these products:
Company of Heroes
Company of Heroes Opposing Fronts
Company of Heroes Tales of Valor
For instance, you only need "Company of Heroes (New Steam Version)", the others no longer work because they are based on the old server. You should delete them unless you have some use for them or you don't mind using that extra HDD space in something you will never play.