Can't Switch Phone to Current Apple ID
I'm not allowed to sign into my phone because it's associated with an old Apple ID that for some reason has been disabled.
iPhone 5c
When you redownload an account's past purchases, use automatic downloads or iTunes Match on a device you can tie the device to that account for 90 days (and similarly on a computer's iTunes) : Manage your associated devices in iTunes - Apple Support - is that what you are seeing ? If it is, and if you can't wait until the 90 days have completed, then you can try contacting iTunes Support and see if they will remove the association : http://www.apple.com/support/itunes/contact/ - click on Contact iTunes Store Support on the right-hand side of the page
Have you tried getting your old account re-enabled ? All of the downloads that you did on the old account will remain tied to that account, so only that account can potentially redownload them, download updates to its apps, and authorise them on a new a computer. You might be able to re-enable the account via 'reset your password' on http://appleid.apple.com
If you are still logged into the account on any iOS devices you might then need to log out of it on them by tapping on the id in Settings > iTunes & App Store (Settings > Store on iOS 5 and below) and then log back in so as to 'refresh' the account on them.
If that doesn't fix it then contact iTunes Support using the link above