A dead TI83+ calculator can be caused by poor electrical contact between the batteries and the main board. The batteries are located in the back cover. The main board is in the front cover. There are 2 pins on the back cover which contact 2 flat copper connectors on the main board. Those pins can wear away the copper and cause a loss of power. The fix is to bend the pins so that they land on good copper.
If your TI83+ is suffering from an erratic or "glitchy" screen, see the video on that topic:
   • TI83 Plus Calculator Glitchy Screen....