How to recover data from MacBook which won't startup properly?

My 2012 MacBook Pro running OS X 10.7 Lion would not start up properly (it has the doomed flashing white question mark on a grey folder). I have tried the following: couldn't access Safe Mode; holding the 'option' key when turning on does not show 'Macintosh HD' only 'internet recovery'; there is no Recovery HD drive present; tried Internet Recovery -> Disk Utility, but my Startup Disk (named "Macintosh HD") doesn't appear in the left column (only SuperDrive appears, and disk0); and PRAM & SMC reset didn't help. I also tried booting a Linux OS from the CD Drive, but it would not boot as there was 'no bootable device, please insert disk and press any key'.

I do not have a backup of this data on Time Machine (my big mistake). My MacBook doesn't seem to recognise the internal hard drive.

Is there a way to transfer the files to another external drive or get my MacBook working again? or is the data doomed to be lost forever?