Internal (Apple SSD) hard drive problem I'm having terrible issues with my Mac since I tried to restore the entire system from a Time Machine backup, which ended up showing a "an error occurred while adding a recovery system to the destination disk" message. I restarted and held cmd+R and Internet Recovery started downloading (instead of booting to the recovery partition). After the download, the menu of OS X utilities appeared and I selected Disk Utility and then I erased the Macintosh HD.

Tried to restore from Time Machine again but the problem persists. I even tried to reinstall OS X: after downloading OS X Mavericks, I got "an error occurred while preparing installation".

Here you can see the results of diskutil cs list and diskutil list commands:

[

As you can see, I have no CoreStorage Logical Volume Groups and I don't see the Recovery HD partition in disk0.
I do believe OS X Base System is the name of the mounted Recovery Partition image.

I would suggest completely erasing every last partition on your drive (except Recovery), recreating a Macintosh HD partition, and reinstalling OS X onto the newly partitioned Macintosh HD.

As for restoring your data, you can use Migration Assistant (/Applications/Utilities/Migration Assistant.app) to restore data from the Time Machine backup after you get a working system, or better, use the "Enter Time Machine" functionality from the TM menubar dropdown.