If you don't want to just turn off Home Sharing on your computer, then two things come to mind.
If you changed the Apple ID somewhere else than the iPod settings - then that would explain things. (I've accidentally cleared the store account when I meant to change this upon going to a friend's house)
I just tested on my iPad and deleting the home share as depicted above immediately disconnected from my Home Share - I didn't need to kill iTunes on the iPad or do any re-starting - the effect was immediate as soon as I exited the settings tab.
Assuming you got the place correct, then your iPad iTunes database is a little corrupt. Sometimes syncing the iPad with a different iTunes library (music only) will delete your music and settings and allow things to work again. It's not easy to poke in the files directly on the iPad - and you may have to restore the device and set it up as new if getting a new set of iTunes data doesn't resolve it.
Lastly - you could check troubleshooting steps with Apple - the express lane at the bottom is good if the steps listed don't resolve it for you. It's highly unlikely to be something on your account with them or the computer, but they will know the oddball causes if the obvious next steps don't work.