Ok, we figured it out.
After uninstalling from Steam, deleting the Call of Duty 4 folder in steamapps, and reinstalling Call of Duty 4 again on Steam, I changed the iw3mp file to the 1.7 version, right-clicked on it, set to Read-only, clicked on the Compatibility tab, clicked Disable fullscreen optimizations and Run this program as an administrator, clicked Apply and Ok. After closing the folder, I could launch my game, change the resolution, download the freezetag mod and map, and finally I could play.
Note: I am not using Punkbuster at the moment, but I have the files. I don't even want to touch it unless I need it, but our servers don't require them.