The screen on a laptop is connected by a ribbon cable, it is not uncommon for some of the wires in the ribbon to break but not all. That could give you the symptoms you describe. Try to move the screen to see if it makes some connection. I had one go a few years back and only half the screen would work!
Since you are only a week out of warranty I would try Dell and see if they will help. Manufacturers don't want a reputation that their products only last the warranty period and so will sometimes offer help for those just out of warranty.
If not lucky if it is the ribbon cable it should not be too expensive to repair.
Good luck