No disk to erase in Disk Utility Internet Recovery
Internet recovery loads from the internet and runs in RAM. Presumably you have more than 1.28GB of RAM. OS X Base System is the base system for recovery, not your internal drive. Based on that, it cannot see your internal drive at all. There's not much you can do if the computer itself can't see the drive. If there's any way you can get this into an Apple Store, that would probably be the easiest solution as I'm sure Apple's technicians could fix this in no time.

On the other hand, if you're comfortable with opening this up and checking for loose wires, then that would probably be my first step (emphasis on MY first step. I wouldn't recommend this to most people).