It doesn't have a private key or anything on it? If not, then it would seem likely that you provided that address to the company you purchased the coins from... so, hopefully it would be included in your wallet.dat that is on your old drive.
If you can open Bitcoin Core with that wallet.dat (regardless of whether or not it is properly synced), you should be able to go to the "Window -> Console" menu... and then enter the command:
It should spit out a bunch of values... you want to look for the one labelled "ismine"... is that "true" or "false"?
If it says "true", congrats, you will be able to recover the coins... if it says "false", you can stop mucking around with that wallet.dat and Bitcoin Coin because it does not contain the private key necessary to recover the coin