Thank you for the additional thoughts. I was thinking of asking if I could take it back to the place where he showed me how to open the case and this last time installed the video card. After the initial installation he connected it and let the drivers install. I assume I could connect it to a monitor there and wait for a while and see if it happens to his.
Taking my monitor to him, I suppose, would be another possibility, but the monitor is heavy and awkward. I'm leery of trying to carry it down the stairs and out to the car. It's tough enough just moving it over to a chair when I have to open the case!
The main thing is that this is an annoyance; it would be nice to have it fixed, but it isn't worth spending a lot of money or doing without it for a while. If it's a symptom of something more serious, then I should have it fixed, but if it's just this, I might as well put up with it. I wish there were a way to find out which it is. I hope this repair person here will have some ideas.
What Gateway did this time was first, have me go to safe mode, and the lines were still there. Then, she had me start up and go to the BIOS, and there were no lines. That's when they decided it was on the motherboard.
Actually, the first one, a week or two ago (by now I've lost track of when anything happened!) was going to send a new monitor, but seemed to think the video card the more likely problem.