A dead TI89 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 pads on the main board. Those pins can wear away the copper pads and cause a loss of power. The fix is to bend the pins so that they land on good copper.
There is a more detailed video on the TI83 plus, with the same contact problem:
   • TI83 Plus Calculator Dead.  Repair.