Graphical glitches and freezing; Logic Board or GPU

The iMac at my shop has been experiencing frequent hangups and failed boots in the past couple weeks, to the point where I can't get it to boot up at all now. The graphical glitches were mostly colored static and what looked like stuck pixels, but I did see some odd box-y artifacts and polygons. In trying to restart we were frequently getting both the folder with the question mark icon as well as the circle with the line through it, but more and more it just hangs at the gray screen. I tried zapping the PRAM, and was unable to boot into AHT, or boot while holding Option. I will bring in my tools to open it up tomorrow, but I just wanted to see what the likely culprits were before giving a recommendation to my boss