TI-84 Plus CE - ON Button Not Working To Turn On or Off

"Thank you for providing all that information! As you guessed, this is definitely a hardware issue. Could you please provide an image of the corrosion (be sure to check if the corrosion is on both sides of the board)? I can see if there’s enough contact left for you to solder jumper wires in place of the traces.

In the meantime, if you have the mini-USB to mini-USB cable the came with the calculator, you can plug side A (the white side) into the calculator and it will turn on. This is similar to plugging the calculator into the charger but this method does not need a power source and also doesn’t clear the RAM.

EDIT:

Alright, I got some help from NoahK. I know you said you checked continuity, but I'll relay that info again. So, the round contacts you see around the button are call test points.

The test point at the top should be continuous with the circle in the middle.The test point to the top right should be continuous with the ‘floating’ triangles.The test point to the bottom left is ground and should be continuous with the outer ring.None of the test points should be continuous with eachother

I know this may be hard to understand through text, so I made a quick color coded picture to explain it:

Shorting the two non-ground pins (the yellow and dark blue in the photo) will turn on the calculator.

Unfortunately, the ON button is special and isn’t connected to the rest of the key matrix so you can’t just connect the button to other keys. I don’t have the info to where exactly the ON button connects to yet."