You can use Lion Recovery to reinstall the OS.
Should also look into how to use the system's tools for backup, restore, manage your system.
MacKeeper is a trojan. If you followed the developer's instructions to remove it, you haven't removed it completely. Follow the instructions here:
IMPORTANT: It’s been reported that MacKeeper has some kind of “encryption” feature. If you used MacKeeper to “encrypt” any of your files, “decrypt” them before you uninstall the software, or make sure that you can restore the files from backups that were made before they were “encrypted.”