Do a backup. Is the installer still in the Applications folder? It should have disappeared if the installation attempt got to the restart point.
Try booting into the Recovery Volume using either command - R or by holding down the option key during restart. Run Disk Utility/Repair Permissions and Verify/Repair the hard drive. If everything checks out, you can then try to reinstall normally.
I would copy the installer before installing and move the copy to a safe place. This will keep you from having to download it again if the installation isn't successful.