There may not be enough memory to run multiple applications at the same time. To speed up the response to touch commands, close unused applications and have only the applications that will be used open. To improve response time while watching videos, have only the necessary applications open for viewing the video and close all unused applications.
Allow the device to charge for 10 minutes before attempting to turn it on. While the device charges, there should be a light next to the power button indicating that the device is charging. If the light doesn't turn on and the device still doesn't respond after 10 minutes, the battery is dead. If the light does turn on then the device may have an unresponsive screen, and the screen may need to be replaced.