if its in your new wallet you will never see it in the old wallet especially if you sent it to an address....reinstalling the software and replacing the .dat file is how you restore or upgrade a wallet with the same coins...looks to me like you sent the coin to an address which is more than likelly in one of the wallets...you might need to do this:
Launch your litecoin client
Click on 'help' in the menu bar (top right)
Click on 'debug window'
Select the 'console' tab
If your wallet is protected by a passphrase (i.e you have to enter a passphrase before you can send) unlock it by typing
walletpassphrase "your walletpassphrase here" 600
dumpprivkey [your litecoin address here]
This will return the private key which will start with the number 5
Once you have your private key if you had to unlock your wallet you can relock it by exiting or typing:
..this will give you your private key for that transaction...then import the private key into the new wallet...use the help command in console if you need the commands to do that....
if your wallet doesnt have a pass phrase then you can just open console and type dumpprivkey followed by the address and it will give you the key