I don’t believe it’s a display problem, I’m fairly certain those lines are just from the calculator booting up. However you can test this by taking your calculator (during the time when it refuses to turn on) and plugging it into your computer (Note, you may need to install TI Connect CE). If you computer recognizes that something was connected, then you’re right, it’s most likely a display issue. If you computer doesn’t recognize that something was connected, then it’s a different problem.
My guess is there’s a loose connection somewhere under the battery compartment. You can follow this repair guide to take the calculator apart (though you don’t need to take out the motherboard) and see if you can spot any loose or dirty connection points.