The first thing I would try is cleaning the screen and/or your fingers (see the trouble shooting guide here). Sometimes dirt can prevent the minuscule amount of current the capacitive touch screen uses from flowing. Beyond that, try resetting your device. If that doesn't work, you may have to replace the touch screen. Good luck!
There are two possibilities here: (1) Some features, like subscription music or videos, use up the battery pretty quickly. If your backlight is set at a bright setting, that would also use battery quickly. See the troubleshooting page for more information. (2) If your battery is very old, it may not hold a charge well anymore. You might want to consider replacing it. Hope this helps!