Since updating to High Sierra all I have is a gray screen.

First my screen started going black and I would have to turn it off by holding the power button. Then it started up one day and shut down, restarted and shut down, this loop continued until I unplugged it. I called Apple who told me to take it to the Genius Bar who told me it was the video card. Too old (2011) get a new one. I did buy a new one but on my new one I did some research and now realize it is from the upgrade. I am currently reloading the original OS from the internet but I had to use the keyboard via usb from my new Mac. neither my new Mac or the old one are recognizing my old keyboard or mouse which have new batteries. Has anybody else had this problem? I failed to mention my old Mac will not boot up it gets partially loaded and then a grey screen.