Do you have access to a second mac which has a Thunderbolt connection and a Thunderbolt cable?

I think you'll need to scratch the drive and re-install the OS. By leveraging the second Mac we can setup your system like a HD to it using Target Disk Mode.

The other option here is to setup a USB thumb drive as a bootable drive using the other Mac system and installing on it the OS installer. Here's the steps for that:

• Get a USB thumb drive (16GB or larger)
• Download the OS installer from the App Store, make a backup copy
• Then create the GUID partition map on the thumb drive and format the partition with Mac OS Extended (Journaled) with Disk Utility.
• Run the OS installer and install the OS onto the thumb drive.
• Once done, copy to it the copy of the OS installer.
• Restart your system holding down the Option key so you gain access to the boot manager select the thumb drive.
• At this point you should be able to reformat the drive using Disk Utility on the thumb drive and using the OS installer on the thumb drive install a fresh copy of the OS.

Do make sure you are connected to the internet as there are some updates your system will need.