Macbook Pro Freezing, Can't back up files either to external hard drive either..

Question

Hi,
I'm not entirely sure what happened but my Macbook Pro, (Lion/Mac OS X 10.7.5) just started to freeze a lot. I can hardly browse the web or sometimes browse folders. In some ocassions its even difficult to  check the Activity monitor or go to Disk Utitlity. I always see the rainbow beach ball of death and in the force quit window I see the red "Not responding."
Because of this issue, I plan on taking my Macbook Pro to Apple but the problem is I can't even back up my files. I just started a time machine and it goes well until in the middle of the transfer it says:
"The backup was not performed because an error occured while copying files to the back up disk.
The problem may be temporary. Try again later to back up. If the problem persists, use Disk Utility to repair your backup disk."
so I tried a different ext. hard drive and still, it says the same message. Upon being fed up of the situation, I attempted to do the old school copy paste from drive to drive but again, in the middle of the transfer it stops and gives me a a differnet message:
"The finder can't complete the operation because some data in ____ can't be read or written."
I checked the file and its a .MOV a video file from my DSLR. I skipped this file and then again, it said the exact same message on a different video file. I can't just avoid these video files. I'm actually a film maker and all this clips are in desparately in need to be backed up.
Does anyone know how to fix this issue? Atleast backing up the files..
Thanks for the help.
p.s.
Not sure if this is related -- since my Macbook Pro has been running slow I deleted a couple of apps such as Things, DaVinci Resolve and FrameForge Previz.. Which to led to having my spolight indexing. I thought it was only the index thats making it run slow but the index done now and I can't back up my files!

Answer 1

If you have more than one user account, these instructions must be carried out as an administrator.
Triple-click anywhere in the line below to select it:
syslog -k Sender kernel -k Message CSeq "I/O error" | tail | open -f -a TextEdit
Copy the selected text to the Clipboard (command-C).
Launch the Terminal application in any of the following ways:
☞ Enter the first few letters of its name into a Spotlight search. Select it in the results (it should be at the top.)
☞ In the Finder, select Go ▹ Utilities from the menu bar, or press the key combination shift-command-U. The application is in the folder that opens.
☞ Open LaunchPad. Click Utilities, then Terminal in the icon grid.
Paste into the Terminal window (command-V).
The command may take a noticeable amount of time to run. Wait for a new line ending in a dollar sign (“$”) to appear.
A TextEdit window will open with the output of the command. Normally the window will be empty. If you get output like this:
kernel[0] <Debug>: disk0s2: I/O error
the boot drive is failing, or there's some other hardware fault in the storage subsystem.