Why can't I use my brother's upgrade key for WoW?

If it works like City of Heroes (and it sounds like it probably does), it is not the computer which is the unique identifier (he could play his ACCOUNT with his paid UPGRADES on additional computers). It is the ACCOUNT itself which is upgraded. It was probably a one-use-only activation code, and so when he added it to his account, it became invalid.

My guess is that even if you entered the code, it would not upgrade your account because it is no longer a valid code. I would further suppose that to attempt use it on a second account might very well be in violation of the ToS (Terms of Service) agreement, which means it could conceivably result in his account being affected.

Yes it is true. Each account needs it's own separate authentication key, not just the computer. If you tried to use his, it would probably tell you that the key had already been used and that you need a new one. I'm not sure about the account suspension, but there is no way you can upgrade with a used key. It's Blizzard's rule.

You have to buy a new game with a new key code. His is assigned to his account. You have to have your own for your account. You can use his discs to dl the games but you still have to purchase the key code.