Chosen Solution

I recently bought a used A1342 as a replacement for my old reliable A1181. Every once and awhile, and without warning (is there any other way?), the screen will go blank (colored blue), and my external monitor will go to a nice purple color, also blank. It’s happened probably a dozen times. It happened once as I pressed play on iTunes, and didn’t appear to have any effect on playing music. Otherwise I’ve had no indication if was affecting or was affected by anything I was running at the time. The past couple of times this has happened, I’ve let it run with the blank screen for awhile, but I’ve always had to force shut it down. It starts right back up and gives me the didn’t shut down properly notice. I assume this a graphics card, logic board or connection issue. What is my next course of action? Serial # WQ0197VSF5W, 2.4 GHz Intel Core Duo running High Sierra 10.13.6, 16GB memory

I believe you have diagnosed it correctly as a failing GPU. The external monitor pretty well confirms that. Not really much you can do, as it is integrated into the logic board. If it were mine i would try a re-flow of the GPU chip using a hot air work station. These can be had for around $60-70. You put the heat on the chip and watch till you see if flow, then pull the heat off and let it cool, then give it a shot.