Installing Mountain Lion from Snow Leopard, Install failed and HD write-locked

I recently downloaded the mountain lion installer from the App Store and I ran the installer. Stupid person as I am, I did not have any backups for my file and I naively assumed that an apple OS installer would be without flaws. Boy, was I wrong. I need every bytes of my data (or close to every bytes) but the installer failed.

Mid installation, the installer stopped and said that the installation failed and that I need to repair my disk. So I restarted the computer and I ran disk utilities (my start up disk was the OS installer and the installer allows me to run several programs, including terminal, disk utilities, and by the way, when I held option while starting up to see which start up disks I have, I only had the OS installer as the start up disk. Also, the installer allows me to run a program called "Startup Disk" when I click on the apple logo on the top left corner, but it doesn't allow me to startup my computer using Macintosh HD) and noticed that when I highlighted Macintosh HD, my "Repair Disk" button was grayed out. So first things first, I ran the "Verify Disk" button but after a minute or so, Disk Utilities said that verification failed and that Macintosh HD needs to be repaired. But the "repair disk" button is grayed out! So I went to the Mountain Lion installer again and ran it. Of course, it failed again so I restarted the computer.

So I tried to first back up all files in Macintosh HD to an external hard drive using Disk Utilities, and I used features such as "New Image" and "Restore" but they both ended up in "Input/Output error". I tried many methods with Disk Utilities but they resulted in errors.

After some research, I noticed that some people's computers worked after they reset their PRAM. So that's what I did. I held command+option+P+R when computer started up and I reset the PRAM. When the start up disk (which is the OS installer, not the normal operating system) loaded, I was greeted with choose languages option and then I was back in the Mountain Lion installer state. I again ran the installer again, hoping something would be different, but then it was different. But not in a good way. When I was told to choose where I would like to install Mountain Lion, I noticed that Macintosh HD was grayed out. Last time, I was at least able to run the installer but this time, Macintosh HD was grayed out. The installer said that my Macintosh HD was locked. After some research, I learned that apparently, the Mountain Lion installer write-locks Macintosh HD mid installation.

So now I am stuck and I am thinking of two things (plus some questions)

1. I am wondering if there is a way to unlock Macintosh HD. But even if I can unlock Macintosh HD, there is no guarantee that the installer will successfully install Mountain Lion, am I right?

a. so how can I un-write-lock Macintosh HD?

2. More realistically, I am thinking of borrowing someone else's macintosh computer and use it as the backup center. I have a firewire cable and a terrabyte external hard drive. So what I'm thinking is that I'll hook my computer in target mode to my friend's computer and I will also plug in my external hard drive to my friend's computer and then I can download and run Carbon Copy Cloner from my friend's computer to copy all data from my Macintosh HD to my external hard drive. And then I will erase my Macintosh HD, freshly install Mountain Lion onto it and then copy all data back from my external hard drive. But I am not sure about few things.

a. it looks like my Macintosh HD is write-locked. Can I still use Carbon Copy Cloner to copy all data from Macintosh HD (in target mode) to my external hard drive?

b. will my computer allow me to erase (or format) Macintosh HD?

c. will my erased/formatted Macintosh HD able to install + be installed Mountain Lion OS?

If you are here, then you have read my long long problem. Thank you very much and I would really really really appreciate your answers and opinions. Thanks