iMac only show flashing folder with question mark after formatting OS X partition drive
This error appears when the startup disk's operating system is corrupt. The safest way to recover the drive's data is to pull it out of the machine and connect it to a different machine. However this is difficult and not likely an option for you. I would try getting someone you know to create a bootable flash drive of an operating system (which system doesn't really matter). You can use this drive to either 1) access all of your files or 2) reinstall a working OS.