Please, I need advice!!!!
My 40g calculator displays the 'invalid card data' message. It blinks and beeps and does not allow me to perform any actions on it. When I take batteries out and back in, it does all the same. The calculator does not react to any key.
Does anyone knows what can be done? Thank you!

From the manual:

Resetting the HP 39G/40G

If the calculator “locks up” and seems to be stuck, you must
reset it. This is much like resetting a PC. It cancels certain
operations, restores certain conditions, and clears temporary
memory locations. However, it does not clear stored data
(variables, aplet databases, programs) unless you use the
procedure below, “To erase all memory and reset defaults”.

To reset using the keyboard

Press and hold the ON key and the third menu key simultaneously, then release them. If the calculator does not respond to the above key sequence, then:

1. Turn the calculator over and locate the small hole in the
back of the calculator.

2. Insert the end of a straightened metal paper clip into the
hole as far as it will go. Hold it there for 1 second, then
remove it.

3. Press ON. If necessary, press ON and the first and last
menu keys simultaneously.

To erase all memory and reset defaults

If the calculator does not respond to the above resetting procedures, you might need to restart it by erasing all of memory. You will lose everything you have stored. All factory-default settings are restored.

1. Press and hold the ON key, the first menu key, and the last menu key simultaneously.

2. Release all keys.

Note: To cancel this process, release only the top-row keys, then press the third menu key.

Oh, Marcus, thank you so much!!!
It really works now!!! Now I actually thought it was something more serious with it!!!

As usual: If everything else fails, read the documentation. ;)

Which steps did you follow to render you 40g functional again?