As indicated by Mr. Rubinov, you may have a potential products liability claim and should consult with an attorney as soon as possible. You should have your pre and post-accident medical records available for review as well as any proof that you actually consumed energy drinks in and about the time of your injury. Since you mention no time frame, the sooner you meet with qualified counsel, the better.
You're not obligated to accept the carrier's decision. You can "appeal" the decision in accordance with the policy or through the NYS Insurance Department or you can bring an action against the other driver. Not sure how much is at stake but you may want to speak to an attorney to get an objective look at the facts and your chances of success.
The posting does not state if your were injured. Assuming you were not, this is probably a question for a landlord/tenant attorney. If you were injured then you take pictures, get the medical treatment you need, report it to the buildings insurance carrier and go see a personal injury attorney in your area. That you agreed to use the service entrance by signing the lease does not mean you agreed to any negligence on the part of the landlord.
The question can't be answered with the information provided. The mere happening of an accident does not mean the hotel is liable. You will have to prove that it was the hotel's negligence that led to the accident and injury. I suggest contacting a personal injury attorney as soon as possible to discuss the hotel's potential of liability. Also, while it would be a gesture of good will, the hotel is under no obligation to provide a free room.