Chosen Solution

When charging, the battery indicator on the screen stays the same at about 3/4 of the rectangle. I left it for about 5 hours and it still isn’t fully charged. When I unplug it to use it for 5 minutes, the calculator battery instantly drops to about 1/4 of the rectangle.

As brandon k pointed out, that behavior likely means the battery is shot and you’ll need to replace it. There’s a guide to help you with that here: Texas Instruments TI-84 Plus CE Battery Replacement Be careful because the battery may have swelled and could cause a fire if you mess with it too roughly.

From what you described it sounds like the battery(s) need replaced.