Most likely the cause of this problem has to do with the battery. I would first check either the Battery Replacement Guide or the Troubleshooting Guide. I would first try to charge the device and see if it shows that it is charging. Then I would use the troubleshooting guide in order to figure out what the exact problem is.
The most likely causes for your problems are that something is wrong with the charger,charging port, battery, or it could be something wrong with the display screen making it appear to be off. You should probably check the Troubleshooting Guide for help. It covers both of these problems. Also if it is just the screen then the Display Screen Replacement Guide could help your problem.
The most likely cause of this problem is either that the screen is damaged or one of the wires got broken when you dropped the camera. You need to determine what the actual cause of the rattling noise is. I would first start by viewing the Teardown for Wire Fixing Guide. If you find that you need more information about anything else, then the Troubleshooting Guide should able to help you further.