Black line appears and then screen goes blank
Your calculator is most likely fine electronically, but the contacts are being interrupted by contamination; it could be water or other fluid, dust, etc. The solution is to disassemble it completely and to rinse it out. Here are instructions for disassembling the TI-84 which should be similar.
If there's water let dry completely before putting it back together. If pop, etc., rinse with isopropyl alcohol (99% alcohol) and let dry completely. The best thing is electronic contact cleaner, available in electronic, auto and hardware parts and supply stores and online. It must be 'safe for plastic' and 'non-conductive', and definitely NOT contain anything like ACETONE. These are harmless to electronics, and my be used to douse any device to clean up all types of contamination, including unseen carbon build-up from normal use. They dry quickly and leave no residue. They can be safely used in any other electronic device and to clean the contacts of old outlets, light switches, etc. -- anything with electronic contacts.
Try to rinse out all areas, especially where the screen makes contact with the main board. If there is any kind of crusty green build-up on the batter posts (due to battery acid corrosion), you may have to carefully rub this with a cloth until you see shiny metal.
Once you've rinsed all the available areas, let dry COMPLETELY (I place a blow dryer (low heat) next to drying parts for several hours to be sure) and put back together.