Q: My new apple ID can't support my old App

Did you create a new account or did you update your existing account ? If you updated your existing account then try logging out of it on the phone by tapping on the id in Settings > Store (Settings > iTunes & App Stores on iOS 6) and then log back in and see if that 'refreshes' the account on it. If you created a new account then any content that you purchased/downloaded via the old account will remain tied to that old account, and only that old account can redownload that content and download updates to its apps and/or make in-app purchases in them.