Hi Wendy! Welcome to WikiTree!
You can learn at lot about your DNA connection to your ancestors by using GEDmatch, but the only way GEDmatch could tell you that you are not related to your ggrandfather would be if your ggrandfather also had a DNA kit posted at GEDmatch.
You are probably comparing your kit to the kit of a slightly distant cousin who is also a descendant of William Andrew. There is no guarantee that you and the cousin would get the same segments of DNA from William. See the tool here.
If you happen to match a couple of cousins who are descended from different children of William, that starts to add to the DNA evidence that all of you might be descendants of William. But lack of a match at that distance doesn't really tell you very much.
Besides, if you are comparing to just one cousin, who knows if it is your line or his that might have some unexpected parentage?
If you want to send me a private message with the pertinent GEDmatch kit numbers and a place i could see the family tree of you and of the cousin, i could tell you more about it.