If you start up Calibre pointing at a (presumably) empty library, and then plug in your Kindle does Calibre see it? If so you should be able to switch to the Calibre device view (by clicking on the device button on the main toolbar) and from there right click the books and select the option to copy them into the Calibre library.
Hopefully next time around you will copy your Calibre library to somewhere safe before reformatting the hard drive
