Is there any way to remove the board from the case?

To begin with, you can follow this guide for the TI-84 PLUS Silver Edition of how to get the backplate off, ignore step 1 and 2 in the guide (don’t know if you can do it on your device and it’s not necessary from what I can see). TI-84 Plus Silver Edition Motherboard and Screen Replacement

A: When you have got the backplate off and it’s looking to be the same as in the guide, then you should be able to follow the guide. Keep a bit extra attention for every step so it’s looking the same as yours, the guide isn’t for the exact same model as the one you have.

B: If it doesn’t look the same, then add a picture of how it looks in your question if you don’t find how to do it yourself. iFixitでの質問に画像を追加する方法