Where on the site can you download wow burning crusade

If you go to your Batttle.net account page, you will see the games you have registered - click on World of Warcraft. Assuming that you already have the game purchased and registered, you can download the client from there.

If you mean purchasing TBC online, you will also find a link to the Blizzard Store on the World of Warcraft website - here you can purchase a download version of WoW and its expansions.

You will still have to use the serial key to register the game to your battle.net account, but should be able to start downloading upon purchase.