I attempted to install CoD4 on my son's Windows 10 computer, out of the box it failed like my Windows 8.1 install.  Try to install normally first but if it doesn't work correctly try below.

I created a folder on the desktop and copied all the files into that folder. Then I went to the \Setup\rsrt directory and right clicked on the Cod4.exe file (if you have you system set to not show file extension it will be listed as an application). Then set it under the Compatibility tab to use Vista compatibility and  run as administrator.  The install then proceeded as it should and asked if I wanted to install a shortcut on the desktop, after I answered this question nothing else happened.  So after a while, it did a Control-Alt-Delete selected Task Manager and then ended the installation.  

At this point the install was complete even though it did not show it was.  Then, installed patches and copied the Punkbuster files over and ran the program.  

The first few times the program ran, it failed to get the list of servers properly.  So you may have to try several time and shut down between attempts. If it still fails to create the list of servers you'll need to use the server list attached to this post.

Go to C:\Users\"your name"\ AppData\Local\VirtualStore\Program Files (x86)\Activation\Call of Duty 4 - Modern Warfare\ .  You should find 2 folders named pb and players and a file called "servercache.dat".  Delete the servercache.dat file and place the one in this post in its place.  When you reopen CoD4 the will be a list of servers already populated there.  Our server is saved as a favorite. The filed is zipped so you will need to unzip it first.