Windows 7: Can't backup my files: unable to access file

I have a Win 7 64-bit and yesterday, I got the black screen of death on boot. Black screen, blinking cursor right after I boot. I can access the Samsung recovery menu. I figured I'd just backup my data and do system restore or clean reinstall. After hours of backup, I looked to see the details on a popup dialogue and apparently, nothing was backed up because it was unable to access the files on my C: drive and transfer onto an external hard drive. I also tried to backup an image, but that also fails. Any help?

First let's try to fix the problem!

Is it a blink cursor, or do you mean mouse pointer? Is it on top left of screen?
just after bios screen, or do you see Windows 7 animated logo?

Do you have a Windows 7 install dvd, or system repair disk (not the factory recovery disc!)
You can create one System Repair Disc - Create from another Windows 7 (64 bits) system. Or borrow one from friend.

Can you boot into advanced boot options Advanced Boot Options
If not... did that ever work before?

If you do a system restore, your own files will not be touched or altered.

If you do a reinstall, you need to first recover your files. Try Puppy: Lucid Puppy way to recover files from a non-bootable computer

I mean a blinking cursor on the top left. I don't see any windows logo when I boot, so I can't log in. I also can't get into safe mode. I have tried system restore, but for some reason, I have no restore points. I have no idea where any of my recovery disks or any disks for that matter. But I do have Win 7 installation on a hard drive given to engineers by our university. Not sure if that would also work.
I'm going to try the lucidpuppy and get back to you. At this point, I just want my files back.

If Puppy does not work for you (although I see no reason why it should not), post back. There are other options.

Okay so I attempted puppy but I kept getting stuck at the last step. It just keeps going and going and I never get the close button to be clickable. How long is it supposed to take? Is my flash drive supposed to be completely empty for it to work?

OK, try something else.

1. Download this .iso from my skydrive https://skydrive.live.com/?cid=475a0...A6D4035%211812

2. Burn the .iso to CD and boot with the CD

3. Make an image of the partition in question - tutorial below

4. Mount the image (double click on it) and extract the files in Computer.

Tutorial: Imaging with free Macrium

How did you try system restore? that's only possible from within windows...which doesn't start in your case. Or did you use a system repair disc, install dvd to do it?