I have been surfing a lot of forums with exactly the same problem, but I found a fixed buried in one site!!!
Firtst you must boot your computer in safe mode, (press and hold F8 as XP boots, if you have a partition tool, press as soon as it has passed the partition screen).
Then enter a administrator account (not limited) and try to install the game, When the Red Alert 2 install window loads and you press the install button, it will seem like nothing happens.
You now reboot the computer, and when you try to install again it will work.
I now have a problem trying to register to play on the internet, but this may be a problem I have.
Hope this helps.