If you have your old computer, you can copy the installed game over to your new one. The CD-Key will be encoded but that version should work until you have to patch StarCraft again. As for the missing key, please check this article - http://us.blizzard.com/support/article.xml?articleId=20639 It may be cheaper to repurchase the game from the Blizzard store instead of mailing stuff to us to get a replacement key.
Tech Support