installation stuck in a loop due to damaged HD
If you haven't already made backups, you can start up from the recovery partition and save a disk image of the main OS X volume (or other volumes you use) to a different drive in Disk Utility.

The first thing I'd try would be to do an upgrade install of 10.7 by choosing Reinstall OS X without erasing anything first. If that wouldn't work, I'd do a clean reinstall and restore files manually.

See these Apple KB articles:


Mac OS X v10.5, v10.6: How to back up and restore your files
OS X Mountain Lion: Reinstall OS X
OS X Mountain Lion: Erase and reinstall OS X