Strange errors, including all files are read-only

This looks a lot like your file system is mounted read-only prior to a drive failure...

So please stop using the computer, shut it down completely and:

1. Open your computer and check the hard disk. If it is not attached to its controller board, then buy a new external hard drive bigger then your current hard drive. It it is attached to its controller board, then buy a new internal hard drive with the same connector type.
2. Insert it in your computer (If it is a laptop, buy an external USB HDD in the step above)
3. Boot an Ubuntu Live DVD and choose Try Ubuntu

4. Press Ctrl+Alt+T to go to a terminal and type:

   sudo apt-get install gddrescue
   sudo ddrescue --binary-prefixes --cluster-size=64 --sparse --timeout=20s /dev/WdX /dev/YdZ
   

   Note : W and X are the drive letters of your nearly broken hard drive and Y and Z are the drive letters of your new hard drive.

5. If that works fine without any errors, we'll be testing whether my gut feeling is right:

   sudo apt-get install smartmontools
   sudo smartclt --scan
   

6. Then perform :

   sudo smartctl /--test:short dev/XdY
   

for all devices that came up during the scan.

Then give feed back please!

Edit: I'm very sorry to have to tell you that your drive is dead.

Please swap the external drive with the internal drive and re-install Ubuntu on the new drive without attaching the old drive. Then hook up the old drive through the USB enclosure and try again... Maybe (extremely unlikely) you can recover some more data off it that way.