If the disk you bought is 32-bit you can still download and burn the 64-bit edition and the product key will work exactly the same as it would on a 32-bit install.
Download Links (if you have Home Premium 32 then download Home Premium 64, if Pro-32 then Pro-64). The file is over 3GB and will take a good while to download so it is best to use a download manager (available as an add-in to IE or included in FireFox) so that if the connection is dropped for any reason it can be resumed.
Where did you buy the product? Does it have any manufacturer logos or educational disclaimers on it, as it may well be an OEM or educational version as Cat mentioned. Unlike full and upgrade versions, the OEM versions can not be transferred to a new computer so if it was installed on another machine then it cannot legally be transferred.
As Cat mentioned, you have some recourse if the product was misrepresented. Also it is estimated that at least 20% of the copies sold on eBay are fraudulent and the product keys will end up being locked out in 2 to 4 months; do not rush to leave positive feedback for such transactions.