What I'd try:
Boot to internet recovery:
1. Power off the MacBook, all the way off.
2. Press the power-on button.
3. Hold down the Command (⌘) – Option (⌥) – R combination immediately upon hearing the startup chime and KEEP HOLDING THEM DOWN
4. You should see an icon that indicates booting to the net.
You -may- need to enter the password for your local wifi setup.
If it boots to internet recovery, you want to open Disk Utility.
Now, you need to select the item that represents your internal drive (NOT a "partition on the drive", but the drive itself).
Next, choose to erase it to "Mac OS extended with journaling enabled" (GUID partition format).
This will NUKE THE DRIVE, back to "nothing on it".
It's now ready for a fresh OS install, so...
...close Disk Utility and open the OS installer.
See if you can install a copy of the OS onto it.
Be aware that the installation may involve one or more reboots and it will take some time.
IT DOESN'T MATTER WHICH VERSION OF THE OS at this point.
All you want to do is to get SOMETHING onto the MacBook to get it booted and running the Mac OS again.
Once the installer is done, you should be presented with a setup screen.
Go ahead and set the thing up, see if you can get an account created and get to the finder.
Does this work?