You didn't tell us which version of the OS.
I suggest you
- power down, all the way off
- reboot to internet recovery (command-OPTION-R at boot)
- see if the OS will reinstall that way.
- if it does, then use setup assistant to access your tm backup and restore, if that will work.
But if it doesn't work...
... here's the Fishrrman "there he goes again, just like a broken record" recommendation:
You are but one more time machine user who has had tm FAIL in a "moment of extreme need".
NEXT TIME, DON'T trust tm to back up your stuff.
Instead, try either CarbonCopyCloner or SuperDuper instead.
Both are FREE to download and try for 30 days.
Try creating a cloned backup on an external drive.
You'll see IMMEDIATELY why it's a SUPERIOR solution.
If you don't like it, just erase it and use the drive for something else.