at start up my system shows a flashing file folder with a ?.

My mac mini shipped with mountain lion, but was upgraded through yosenite. Recently some local construction has cases a bunch of power outages. At start up my system shows a flashing file folder with a ? in it. I talk to some people that suggested the OS was corrupt. The repeated power outages not letting the system shutdown properly is the only reason I can think this might happen. They suggested I try system recovery, which I did. However, I'm not able to restore the OS as recovery can not seem to find the drive to restore.

I'd appreciate any help I can get to get the system back up and running.