Hmmm … could this be hardware afterall? Can you disassemble and reassemble the screen (here’s a nice video)?
Else there’s still the OS … the so-called “factory reset” is no real factory reset, as it only removes all user stuff and Apps and leaves the OS as is. If there’s something wrong with the OS, there’s still the option to completely wipe the phone and install the OS from scratch.
But first try disassembling the display, it’s much easier and faster 
.