now when I reinstalled bitcoin (on the same computer) my wallet is actually a different address.
Just to clarify, with the Bitcoin.org client you don't have "an address", you have a wallet that contains many addresses. Each time you click Receive money a new address is generated. So just seeing a new address doesn't mean anything
Also, installing the client again doesn't overwrite or replace an existing wallet.dat
The wallet.dat contains the private key for each address in the wallet. Without those private keys, you can't spend the funds.
I do not have a backup (or the one I had apparently has no coins),
You can click on the Transactions tab to see all activity that occurred. If it shows no activity at all, then for whatever reason it is currently an empty wallet.
Also, until the blockchain sync has completed, your balance shown by the client may not show properly.