I don't think a factory reset will work. It sounds like a hardware problem. Either the display, it's driver, or the ribbon cable connecting the display to the mainboard has gone bad.
If you want to try a factory reset, your could boot into stock recovery and do it from there, but if you have no display even during bootup it will make it more difficult. Watch this
YouTube video. Ignore the fact that it's from a website called rootjunkie. You DO NOT need root to get into recovery.
Without a display you will have to do it with buttons only.
Power off, if you can't just remove the battery for a few seconds, and replace.
Home, Volume Up and power - reboot into recovery (timing may be an issue here, releasing the Power button)
Volume down 3 times - scroll down to factory reset
Power button once - select Factory Reset
Volume down 7 time - scroll to Yes delete all (may be an issue, I haven't used stock recovery in a LONG time, I'm not sure if it's always at that position or not)
Power button once - select Yes
Wait - it may take longer than in the video for a factory reset, so wait at least a minute before continuing
Power button once - reboot
Wait
Watch the video before attempting to see what is happening.
If successful, you phone is reset as it was when it was first taken out of the box. Everything is wiped except the external SD card, if you have one installed.
If you still have a black screen, it's definitely a hardware issue. About the only thing you can TRY if it's hardware is to reseat the ribbon cable to the display. It involves some disassembly if the phone. See the teardown of the
S3 here. In the photo next to step 5 the ribbon cable connector is the small beige rectangle with the yellow ribbon cable to the left of the SIM and SD card holders. Pry it straight up to remove it then center and press it back down. Reassemble and boot up the phone. It's a longshot, but it's the only self trial before sending it somewhere or trying to replace the screen yourself.
