Do you have any friends who have discs?
The discs themselves are totally sharable, and since you've already bought the game, and already have a BC activated account, the Disc Key doesn't matter. The Key is tied to your account, proving that you've bought the game and have a valid account.
Remove the info that you've got from the partial install, and borrow discs from a friend. If they don't have the discs, or can't find them, here's another neat trick:
Get onto a Local Area Network with them, or bring an external hard drive over to their house. Then, ask them to share their WoW folder. You can either copy their WoW folder and paste it onto your computer, or put it onto your external hard drive and bring it back to your computer at home.
All files are valid, in-tact, playable and legit. You'll be able to play as soon as the whole folder is on your computer.
If your BC discs are fine, and you're JUST looking for World of Warcraft, go to a game store and pick up a World of Warcraft DVD (around $3-5). It says "Free Trial" but it has all install discs burned onto a DVD.
Best of Luck,
Personal Experience, done many times.