IOS – Recover data from locked iPad

Your question can be rewritten in short form:

1. iTunes: How to move your music to a new computer
2. Where are my iOS backups stored? - expand the section About Syncing and Backups and you'll see

iTunes places the backup files in the following places:

• Mac: ~/Library/Application Support/MobileSync/Backup/
• Windows XP: \Documents and Settings(username)\Application Data\Apple Computer\MobileSync\Backup\
• Windows Vista and Windows 7: \Users(username)\AppData\Roaming\Apple Computer\MobileSync\Backup\

I linked to the official articles since things do change and cutting and pasting the steps today might not be right if things change in a month or two. Don't worry - the article about music moves everything except the iOS device backups. If your device is working, there's no need to move backups unless you want to keep older ones or save time the first time you sync with the new iTunes.

This is a little like what happened to me, I posted a question here relating to notes that had gone missing too.

It seems that if you take a note while offline, when you sync with icloud it will sometimes without warning delete notes it does not know about :( Luckily in my case since I had made the note on my mac it created a recovery folder for me.

Perhaps your phone may have done a similar thing? If you open notes and hit the 'accounts' button at the top, is there a 'recovered items' folder?