IF I'm understanding you correctly, you own the following versions of the game:
Vanilla: levels 1-60
Burning Crusade: levels 60-70
Wrath of the Lich King: 70-80
If that's the case, all you would need to do is buy Cataclysm and add the key-code to your original account through Blizzard, by original I mean the account that shows you've purchased all the predecessors to Cata. Installing Cataclysm should install the whole game, however, the launcher might update with the latest content patch.
I hope that helps.