How to reinstall data after Maverick upgrade

I attempted to install Maverick last night and the installation got hung up to the point it ran all night saying "less than one min" remaining. I finally had to force shut down my mac this morning and when it rebooted, it took me through the set up steps like it was a new machine. It asked me if I wanted to restore my data and after many attempts with my Lacie HD connected directly to the Mac, it would not even recognize the drive so I had to bypass this step. I am now trying to figure out how to restore my back up data onto my mac. My backup was on mountain lion and the machine has 10.9 on it now. I have a time machine back up but also another backup that is in a start up disc format I believe. Whats the best way for me to get my system restored? Can I just revert back to mountain lion and see if it will recognize my external back up drive?