Blinking folder icon - safeboot, recovery hd does not work
Did you do anything special before the problem showed up? Like performing an osx update? I'm asking because I experienced my SSD going completely dead after an osx update myself before.

It might be the disk is broken, especially indicated by the disk not showing up in internet recovery.

If you feel comfortable with it, I'd advise you to boot up a Linux live distribution of your choice and check if it is able to detect and mount the drive. If it's not detected, professional disk recovery services are likely your only chance. If Linux is able to mount or at least detect it, you should be able to repair it or at least rescue your data. There are tons of sources on how to repair/rescue hfs+ partitions from within Linux, such as this.

If you don't want to go this route, you can always head to your nearest Apple store and let them determine the issue. While they might not fix it (for free), you'll at least know whats going on and if data recovery is an option.