Two choices:
1)
Go back to the iTunes library folder and move it to some other folder. Open iTunes and it should create a new blank library.
Go to Preferences and make sure that Keep iTunes Media Folder Organized, and Copy files to iTunes Media folder when adding to library are checked.
Now go to the Files menu, chose Add to Library, and navigate to the folder(s) containing the music. Import them.
Never fiddle with the folders again, unless you need to recover like you are now.
2)
Of course, this only applies if you are willing to give up manually managing where you music is stored. But you're going to lose that ability if you use Transfer Purchases to copy your music back to iTunes anyway; which is the key to what you actually asked for.
That option can be found by right clicking on the iPad in the Devices list in iTunes. Just say no to all the erase dialogs and stuff until you've done that step and made sure your media has been copied back to iTunes.
1.1)
You might have to use Transfer Purchases anyway, even if you use the first method. It's the main way to get iTunes to recognize a new iPad without erasing it.
3?)
There are other computer programs that will copy your music library to your computer. I'm not familiar with any of them, but a Google search should turn up a few. Research them carefully.