Recovering Pictures and Videos

I have an iPhone 6+ that overheated on a charge on an Apple cord and charger. I cannot get this phone to turn on whatsoever even with a hard reboot by holding the home key and the on button. I pulled that SIM card out of it and plugged it into my 5C to reactivate that for a bit and that worked until I accidentally pulled it onto the floor last week! I have used a previous backup that had these pictures from iTunes before when it went down on me and had to be restored that way however, that backup no longer exists. Apple claims its not there even tho I distinctly remember restoring my pictures from it before. Any way I've already tried one of the data recovery software programs out there that claimed they can connect directly to the device and pull it off. This phone will not turn on. The computer will not even acknowledge that I have it plugged in that is how dead this phone is. Its out of warranty and I really don't want to spend the money to get it fixed as I've moved on to an Apple 7+ but, I would like to get the pictures and videos off that phone. They should have backed up to the cloud when I backed it up but they're not there. I know they were on the phone when it went down. Is there a way to retrieve these pictures or do I have to consider them as lost?