Does the warranty cover the camera if it was dropped and the screen broke?

If it's due to impact damage, I'd say not. Most warranties don't guard against what honestly is negligence, even if it was accidental. And dropping a camera can cause impact damage. Sometimes, however, you can still get it repaired under warranty. I'd send it in for a warranty repair and see what happens. If they don't repair it, they'll tell you how much it would cost to fix. The rule of thumb is that if the estimate for repair is north of 50% what you paid for it, you're better off taking that money and buying a newer and upgraded model. But at least you'd know ...