Hi there and welcome
Can you do the following please
Tell me if it then starts correctly please.
ok, can you do the following please
What then happens?
Reboot into the Recovery HD by choosing the ‘Apple‘ menu > Restart, then hold down the ‘Command’ + R’ keys on the keyboard during the start up process. When you see the Apple Logo you can let go. When the machine boots you may have to choose your language then you will see the OS X Utilities screen. Select the Disk Utility and then select Continue. Then in Disk Utility select Macintosh HD in the left column (if there are two with that name or it is named something else choose the first indented item) and then Highlight your hard drive and on the right select the First Aid tab if it is not already selected, then click on Verify Disk on the far right. If that says “OK” in green type then select Repair Disk Permissions. If all is ok quit Disk Utility and select Reinstall Mac OS X.
Did you check it with Disk Utility first?
OK there is no point in restoring from backup or doing anything else until you can get that disk verified and then either repaired or reformatted. Restart and hold the Option or ALT key until you see a list of boot partitions, if the Time Machine drive is connected you should see it as a boot option. Choose that to boot from then use the Disk Utility on the TM drive to check Macintosh HD. Let me know
Where you able to get the disk verified? Please let me know