I have a 2010 iMac 21 inch model the screen has started this weird screen problem shown below and I wonder if this would be a heat related problem or a logic board issue.
Looks LCD-related to me, no GPU. Physical issues, possible internal cable. If you hook up an external monitor does it come out clear? is the mac locking up or just the screwed-up display picture?
Can you targe display mode that modle? if you have a MacBook book that might be another way to confirm its the screen itself.
Honestly, it is a 2010, it might be time for a new one
It locks up the machine most of the time as well. It may run for hours then start this screwed up screen then it will lock up.
It will do it pretty quick if playing a dvd or a YouTube video full screen.