Finding a games CD key?

I recently installed my old copy of Call of Duty 2. My brother had thrown out the case along with the key code for it for no reason other than to annoy me :cry. The game prompts me for a CD code so the CD code is probably stored somewhere on the game disc itself just hidden and id have to write down the same code for it to work. Any way I could find my CD code by opening up files on the disc I have and finding it? Please help me.

 

Edit: I dont know how to actually edit so I post again. I actually bought the game and have it and have the disk just dont have CD key so its not me trying to get for free, its just very old so thats why box is thrown out. I can supply pictures so people dont think im trying to get it for free.

 

Update: I used a winzip to extract the data.CAB (which supposedly contains my cd key)file to desktop but still not getting what to do with it now so still using the one written in disk. Winzip cant open the file because its not a valid archive (no idea how to use winzip just was clickling unzip). So I looked online and it said to use extract.exe and I tried using that on a .txt file and a .doc file but it still says "Can't open output file: C:\Files\RW\cod.txt" etc.. Somewhere online it said to make the files read/write so I right clicked properties but they always revert back to read only box after every time I press ok and right click again. No idea what to do am stuck here after searching around on the internet, please help me

 

Activision's official stance on lost CD keys:

This is the worst possible form of customer care I've seen from a PC game developer in a long time. If you own the game and can prove it, they should be willing to help their customer, not force you to buy a new copy. Then again, this is Activision. I should not be surprised.

I say your brother owes you a new copy of CoD2.

EDIT:
Try using 7zip instead of WinZip to extract the cab archive. It's much more versatile.