I think you are better off purchasing a new USB stick. In the long run it may be cheaper after shipping, cost of repair, and still having to use something that is 7+ years old and may fail again. If you do repair the gameport/analog stick, keep in mind the newer pots run much better than the older ones they used in their gameport products and they'll put it one of the new ones if the bench goes poorly.
Again, I'd recommend buying a new one (Provantage is usually the cheapest).