If Civ IV Vanilla and BtS are installed separately, maybe you will need the linked Civ_BtS_DLLs.zip to play Vanilla?
Is it possible to place a Steam install completely outside Program Files and your user documents areas? Windows can place extra restrictions on files that get placed in such "special" locations. For example, can you install to C:\Civ4\ or somewhere like that?
Have you tried running Civ IV in compatibility mode? Perhaps try Windows 7 compatibility mode, if that option exists, or Win XP, if Win 7 doesn't exist. Presumably, if you create a Windows Shortcut, you can right-click on the Shortcut, choose Properties, and then on the Compatibility tab select one of those Operating Systems along with running the program as an administrator.