Installing Yosemite failed, and it turned my disc into "read only"

Question

Tried to upgrade my MacBook Pro (Early 2011) to 10.10 from 10.9.5 AppStore. It failed after reboot. Then the disaster began...
(Yes, unfortunately I didn't backup...)
My disc became "Read only":
I couldn't install 10.10, neither reinstall 10.9.5.
Tried to repair the disc and permissions with 10.10 Disk Utility, both failed.
Tried Disk Utility in 10.9.5 recovery, it says "unable to mount the disc".
Tried to use Disk Utility "Restore", to copy the entire volume to another disc, it gave me "Could not restore - Input/output error",
Tried to create a new image from that disc, still Input/output error.
Then I used a new disc, clean installed Yosemite on it. However, I couldn't migrate my data from the old disc. In Migration Assistant, it couldn't find any source. (Tried to connect to another disc with clean installed Yosemite, Migration Assistant could find it)
When I tried to simply copy "all files" (including all hidden files) to another empty disc, I always ended up with "The operation can’t be completed because you don’t have permission to access “some file”." ("some file" changes every time).
Thai disc had been working for over one year without any problem, until I hit "Upgrade to Yosemite"...
It's been a week now, and I have no idea what else I can try to repair my disc / make it writable again / migrate system information from that disc... Please help!

Answer 1

First, look at this article and see if your model can do an Internet Recovery: Computers that can be upgraded to use OS X Internet Recovery. If yours needs the firmware update, then do that  before moving on.
Install Mavericks, Lion/Mountain Lion Using Internet Recovery
Be sure you backup your files to an external drive or second internal drive because the following procedure will remove everything from the hard drive.
Boot to the Internet Recovery HD:
Restart the computer and after the chime press and hold down the COMMAND-OPTION- R keys until a globe appears on the screen. Wait patiently - 15-20 minutes - until the Recovery main menu appears.
Partition and Format the hard drive:
Select Disk Utility from the main menu and click on the Continue button.
After DU loads select your newly installed hard drive (this is the entry with the mfgr.'s ID and size) from the left side list. Click on the Partition tab in the DU main window.
Under the Volume Scheme heading set the number of partitions from the drop down menu to one. Click on the Options button, set the partition scheme to GUID then click on the OK button. Set the format type to Mac OS Extended (Journaled.) Click on the Partition button and wait until the process has completed. Quit DU and return to the main menu.
Reinstall Lion/Mountain Lion. Mavericks: Select Reinstall Lion/Mountain Lion, Mavericks and click on the Install button. Be sure to select the correct drive to use if you have more than one.
Note: You will need an active Internet connection. I suggest using Ethernet if possible because it is three times faster than wireless.
This should restore the version of OS X originally pre-installed on the computer.
If for some reason your hard drive cannot be repartitioned or is not even visible in Disk Utility, then the drive has failed and needs to be replaced.