First try replacing the coin cell battery and the AAA batteries.
Second, press on then repeatedly press 2nd then the up arrow to increase the screen contrast.
If neither work then there's likely an issue with the display ribbon cable. It's very common for the ribbon cable on old TI graphing calculators to degrade over time and break.
You can test if the display still partially works by pressing:
If the calculator itself is working then this will launch a self test. I show how this works on a TI-81 which is similar to the TI-82: https://youtube.com/shorts/eX6TeJkKNtQ
Press enter 3 times, then press on.
Continue pressing enter to cycle though each test. If you see the display suddenly show something then you know the calculator itself still works but the display needs repair.
If you press it 16 times without seeing anything on the screen then either the cable is completely broken and needs repair or some other component broke and it will require hardware troubleshooting I'm not qualified to walk you through.
The ribbon cable can be repaired by soldering wires across it, bypassing the broken traces. There's more info here: https://www.cemetech.net/forum/viewtopic... (thankfully the TI-82 is a bit easier to repair than the TI-83+).