Because the headphone jack is attached to the logic board (soldered on the logic board), replacing the headphone jack might require special tools and extreme care. It might not be a good idea to do that unless you have all the necessary tools and are willing to take the risk.
check this link on Step 10: iPod Touch 1st Generation Logic Board Replacement
Dave, I agree with Bac that it sounds as if few connectors inside the headphone jack got loose or bent. You can check inside the headphone jack using a small keychain flashlight to see if it's true. You might find something tiny but strong enough to bend the connector back to its normal condition if the connector's bent. I know it's not that easy to do, but that's all I know.
Hope you can get it back to work normally.