Examine the contact pads for corrosion.

To test if the corrosion is causing the calculator to not power on:

Place good batteries in the back of the case (proper direction)

Lay the circuit board over the batteries (4 little posts will align them)

Press down a little over the batteries to make sure they have a good connection (if necessary)

Tap a screwdriver to short the "ON" contact pad (top right)

If the display comes on, then the corrosion is the problem

Follow the same steps for testing if the corrosion is causing a key not to work. Except short the contact pad for that key to test it.