try looking under your intuit account, sign in here (not the "sign in to turbotax" that takes you to TT online)
https://accounts.intuit.com
then under your account management page try "Products and Billing" on the left then click turbotax and it should show you all the versions available to you and the license keys. Not sure the criteria for storing this info if it depends how you purchased (download vs. CD) or registered the product but this is a good place to start.