Do you have a friend with a Mac? If you do you'll need to visit them with a USB thumb drive and a good bottle of wine or some beer ;-}
What you'll need to do here is setup the thumb drive as a bootable drive and copy over it the OS installer your friend can download from the Apps Store if they haven't already downloaded it.
Using Disk Utility delete the current partition (likely FAT32) and create a GUID partition map and then create a Mac OS Extended (Journaled) partition. Once that is done you can run from your friends Mac the OS installer and select your thumb drive. Once done, reboot your friends Mac and hold the Option key so the boot manager comes up select the thumb drive to get it to boot up once up copy the OS installer you used over to it. Shut down the Mac so you can take the drive off.
Now to repeat the process on your Mac's hard drive. Of course finish the wine or beer first!