Based on history, it is probably the graphics hardware. You cannot reset that. On the 2010 iMacs, the video hardware is an actual socketed card and theoretically replaceable. However, working cards for that model—when you can find them—often cost more than a working 2010 iMac is worth on the used computer market. If your cannot do the work yorself, the labor costs could double the cost of repair.
You can try attaching an external monitor. Itf the image is there, you know the problem is not in the graphics card and more likely the display itself, its inverter, or the display cable.