For a week now, when I turn on the camera, the back screen shows up with vertical red and green stripes. The videos I record come out fine, so the sensor is working properly. Is it a screen defect or something I can fix without going through warranty?
It's most likely a fault with the LCD screen itself, not the sensor or anything you can fix yourself! Since you're saying the videos come out perfect, you can rule out problems with the camera's internal electronics. Color stripes like that are usually a sign of damaged pixels or a bad connection in the flat cable that connects the screen, and that almost always means you need to replace the entire screen. If your camera is still under warranty they'll swap it out no problem, but if not, see if you can get it done for a decent price at an authorized Nikon service center.
Have you tried restarting the camera or resetting it to factory settings? Because before assuming it's the screen itself, there are a couple of things you could try without risking anything. Sometimes those lines show up because of a software conflict or a loose connection in the cable that connects the screen to the motherboard, and in those cases a reset or even turning the camera off for a while and taking the battery out can surprisingly fix the problem! If the lines are still there after that, then it's likely a physical failure of the LCD screen, but honestly the whole "you can't fix it without warranty" thing depends on how long you've had the camera and where you bought it from, so it's worth checking those options first.
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