I don't know if this is the answer, but try a 1.6-1.7 patch. That's what it's called.
I got mine from xfire because I trust it more than anything I'll find on FileFront or other sites.
http://www.xfire.com/downloads/3228/If you don't like xfire for your downloads, google
1.6-1.7 cod4 and there are several places to go.
I don't know if it's related, but I had trouble after downloading the patches individually (1.6 and then 1.7) so uninstalled them and got the "combo" and it worked after. Others, probably most, downloaded them individually though. Or maybe I never uninstalled them in the first place and the problem was separate.
This is why they keep turning down my JANE's Tech Support Corner idea.
EDIT: Oooooh. Found this:
THIS [v1.7] PATCH IS INCREMENTAL: You will need patch v1.6 installed for v1.7 to work.Well, I don't if the 1.6-1.7 thing even matters, or if it's both patches or what, just that it somehow worked for me. But I must have DLed 1.7 first and had trouble and no one else did. So download 1.6 and then 1.7 and I guess that should work. 1.6 is the "main" patch (added new maps, fixed a few probs), while 1.7 fixes things that was wrong with it, that's why they both have to go together, with 1.6 there first.