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First question is how do you back up iPad now? Do you have another computer? If so, is it on the same network as laptop? You can open iTunes in both and enable home sharing and then music will be on both.

If not here is a link to reinstall iPad to laptop and save your stuff on it. But then the laptop will be your default device to backup iPad.

http://support.apple.com/kb/HT1848

That's the only 2 ways I know of to getthe music from your iPad.