This is the exact problem my son's friend had with his MBP. An Apple Tech acquaintance suggested it was the hard drive, but since I could Target Disk Mode his files to my Mac Mini, I really didn't think so. I changed it anyway, with no luck. I did a lot of googling, and decided it was the hard drive cable. Used the excellent help found here, and installed a new one. It works!
Answer to: Hard Drive not recognized by system during boot or install