If not already connect your Mac to your router via a cabled connection rather than through WiFi.
If your computer will support it, try Internet Recovery. Try booting into Internet Recovery (command - option/alt - R on a restart). It is a slow process. This will install the newest OS that the computer is compatible with. Reformat the drive using Disk Utility/Erase Mac OS Extended (Journaled), then click the Option button and select GUID. Quit Disk Utility. Then install the OS.When the computer restarts, you can use Setup Assistant to restore your data from Time Machine.
If your computer will support it, try Internet Recovery. Try booting into Internet Recovery (command - option/alt - R on a restart). It is a slow process. This will install the newest OS that the computer is compatible with. Reformat the drive using Disk Utility/Erase Mac OS Extended (Journaled), then click the Option button and select GUID. Quit Disk Utility. Then install the OS.When the computer restarts, you can use Setup Assistant to restore your data from Time Machine.
OS X Mavericks not reinstalling on my MacBook Pro.