Mega 2560 being powered by 5V on any pin on the board

Hello, I am trying to use pins 2 and 3 as external interrupts on the arduino mega 2560. I have noticed that even if there is no power being supplied through the usb or external voltage, the board will turn on if I connect a 5v input signal to one of the interrupt pins (or any pins other than gnd) . Does this mean that the board has some short circuit somewhere, or is broken? Any ideas would be helpful.

Don’t do that. You are not supposed to connect 5V to the input pins when without power to the board. I don’t know what you mean by the board “will turn on …” Did you load any code onto it and then try to run it without the USB cable to see it is really ON with your 5V connected to the interrupt pin ? Did you do that ?

Current is flowing thru the pin protection diodes to power the chip.
The diodes are only good for 1mA, you risk damaging them if you apply signals with Vcc being applied.