If you make a .reg file and put this in it, and then run it, it'll change your key. Make sure to replace the red text with your actual CD key, including hyphens.
If for some reason you're on a 32-bit PC, delete "\Wow6432Node".
Unless you're playing on Steam, then you should already have a unique key installed.
[HKEY_LOCAL_MACHINE\SOFTWARE\Wow6432Node\Unreal Technology\Installed Apps\UT2004]
"CDKEY"="1234-1234-1234-1234"