OSX Start Up Disk & Restore Failure

Hi Apple Support folks,

My late Macbook 2010 supporting OSX Yosemite has been experiencing random system reboots with missing keychain pop up windows appearing during start up. After a morning of working in the garden, I came back to my laptop in horror as OSX Disk Utility Startup has activated and wants me to re-boot/re-install my hard drive. After checking online for support from the community, checking disk utilities to repair and verify my disk drives which are in good working order, even trying to reinstall Yosemite OSX from scratch or booting from Time Machine I am unable to do. Ultimately, all my feats of trying to recover my data or even starting Yosemite from scratch seems restricted and futile. I am now face to face with a Macbook that is Inaccessible, with all pathways in Disk Utility Startup tried and failed...

Here is a past question found on the support forums that sounds similar to my situation: Imac won't restore from time machine backup after HD (hard drive) recall replacement.

Although my scenario seems worse due to the fact that I am unable to restart and reinstall my start up disk from scratch or find any time machine backups

My only other thought is to find my missing external hard drive and hope that I can Start up from there

Thank you so much for your time and support : )

I look forward to hearing from you!