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#11
You generally don't have to reinstall Linux to get it booting again. With Ubuntu, you can reinstall GRUB directly from the CD without having to reinstall the entire OS. Don't know what options Mint provides, but it would be worth your checking on their forums to see if they have a similar capability.
Also, with Ubuntu, once you have the Linux drive booting, you would reconnect the Windows drive, but continue to boot from the Linux drive, open a terminal, and enter "sudo update-grub" -- to regen the GRUB menu and add an entry for Windows. You should check for this on the Mint forums as well.