The TI 83+ calculator is comprised of 2 board. A main board which contains the processor and buttons and a smaller board that contains the LCD screen. These 2 board are connected with a flat cable. This cable has a high failure rate. Symptoms are abnormal characters, lines, drop outs etc. A glitchy screen.
This video shows how to remove this cable and replace it with jumper wires. Soldering is required.
If your TI83+ is completely dead, you may have a bad battery contact. That is covered in another video found here :    • TI83 Plus Calculator Dead.  Repair.