If you have AppleCare, repairs should be covered, regardless of cause. The most you MIGHT have to pay for a damaged display in the US is about US$100.
But it will take an in-person inspection to determine what the actual problem and a solution might be. Under AppleCare and also under the one-year warranty, defects in materials and workmanship are covered completely.
If you have an Apple-owned store available, they will provide an inspection (but you MUST make an Appointment) for free, in warranty or out.
If your support is provided by Apple-Authorized Service Provider, they may have an evaluation fee. This is to keep users from consuming their expensive technician time with frivolous problems. If the make ANY repairs that you or Apple Pay for, ask for a refund of the inspection fee.