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My math teacher knows that know a little more than average with calculators, and asked me if I knew what was wrong with one of my schools Ti-84 Plus calculators. When you turn it on, there are 6 verticle lines running down the screen. Once you perform about 6 calculations, it changes to 12 broken verticle lines. I have tried resetting the ram and archive, but once you go into those menus, it becomes so distorted, you can't tell what is going on. If you have any idea what is wrong with it, I would really appreciate it.

Pictures: https://imgur.com/gallery/QJWr7
The Ti-83 Plus makes use of two ribbon cable assemblies on the inside which control the display. The ribbon cables are infamously unreliable and it is likely the situation you have on hand.

An example picture of the calculator insides: http://www.datamath.org/Graphing/JPEG_TI-83PLUS_I0799.htm#PCB
The insides look more or less the same for most ti-83 plus calculators. The screen condition you have looks like the bottom grey ribbon above the four IC's has failed. That cable is used to transfer data to the display board and when the conductive glue connecting it decays, you get distortions on the screen.
Refer to this post for repairs to the ribbon cable: https://www.cemetech.net/forum/viewtopic.php?t=5161&start=0
On the other hand, the large black tape piece at the top is the upper ribbon cable which is nearly impossible to repair without specific equipment. That doesn't look like your issue from my experience.
  
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