Simple Key-Led design does not work

Also check the logic levels your switches/leds are using. Often switches have pullups and pulls the signal to GND when pressed. The led could also be connected between VCC and the FPGA output - i.e. ligth when the output is 0. If this is the case you would see the behaviour you describe since you have implemented two "or" functions. Negating all inputs and outputs gives and "and" function instead. Easily tested by pushing all switches - your leds should ligth then.