Internal (Apple SSD) Hard drive issue

So, you're dead in the water and cannot get to your Desktop?

What model and year Mac do you have? Desktop? Laptop?

Ok so I would do the following before concluding my SSD is failing or failed.

Shutdown.

Unplug all external drives and hubs.

Perform a PRAM reset. Power on while holding Command+Option+P+R and KEEP them pressed until you have heard the boot chime twice then release. The Mac probably won't boot to an OS and you may have to Shutdown again the restart holding Command+Option+R (Internet Recovery).

Launch Disk Utility and select your Macintosh HD. Then do a Verify Disk. If there are any errors, do the Repair Disk. If no errors appear, click the Partitions tab and select the Macintosh HD. Use the Partition Layout dropdown and select 1 partition. Click Apply. This should recreate your partition, erase and format it to Mac OS Extended-Journaled with the GUID Partition Map Table.

Quit Disk Utility and Reinstall OS X which I think you said is Mavericks which came pre-installed. IF.. the install completes, you should have a Mavericks Recovery HD and be presented with the Setup screen. IF... the install throws out an error, can't complete, won't create the Recovery HD, etc. then you may want consider either setup a Genius Bar appointment at a local Apple Store to have them diagnose the drive issue or try Internet Recovery again and install to an external USB drive just to get an OS installed. If the external drive install works with no issues then it's very possible your internal SSD drive has failed and needs to be replace.

That looks like it's an internet connection issue. If you can use an ethernet cable and try again or make sure your WiFi connection is solid.

So, I would Shutdown, wait 10 seconds and try Internet Recovery (command+option+R) again with an ethernet cable.

Core Storage is the new way forward and only mission critical for using Fusion drives and FireFault2. Other wise no difference really—and still has some notable shortcomings esp in Disk Utility. You can easily convert to CS on the fly using terminal and simple reboot.

Restoring from time machine can loose the CS and leave you with classical.

New install of the OS should restore CS.

http://blog.fosketts.net/2012/10/03/mac-os-corestorage-convert/

http://apple.stackexchange.com/questions/175781/is-undoing-yosemites-corestorage -conversion-dangerous

https://www.reddit.com/r/osx/comments/2wzlxc/a_corestorage_primer_aka_why_you_ca nt_manipulate/

So the only problem is you do not have a recovery partition?

Re-installing the OS X on top, should replace the recovery partition and convert to CS.

Stop using your Time Machine back up to restore your entire system. It's obviously not working. What you need to do is check the disk using Verify Disk and Repair Disk to repair any errors. Erase and reformat the Macintosh HD. THEN reinstall OS X Mavericks. After you get Mavericks reinstalled then during Setup you can try your Time Machine back up to migrate your user accounts/settings/data and apps using the migration in Setup.

You're not going to know if the reinstall of OS X will work unless you try it. So, you either use Internet Recovery, because your drive is empty, or a USB thumb drive with OS X Mavericks installer (which I doubt you have) to boot from.

Keg55 said it best above.

If you have the OS running, reinstalling the OS again ( on top of your existing) can sort some problems.

Not having the recovery partition is a minor detail and not mission critical.