OS Yosemite installation "

I am hoping you can help me with my issue. My MAC has been running fine until I decided to upgrade to OX X Yosemite. When it is installing I get the message.

"File system verify or repair failed".

I clicked the restart option to boot into my internal HD but tells me its unavailable.I then rebooted, held command/R to enter disk utility in order to repair the disk, but it tells me it failed and should backup and restore the HD.

I then tried to create an image on my external drive but this also fails with the message "Unable to create Macintosh HD.dmg. (Input/output error)"

I am stuck in this vicious cycle of restarting and the installation failing. I cannot escape the installation process. Is there away to access my files and copy across which ones I need onto my external HD then erase and restore the internal HD?

Many thanks