Pull-down resistors on 7447 input pins
As others have pointed out, your pull-down resistors don't work because they aren't pulling down hard enough. So what value do they need to be to do the job properly?

The SN7447 datasheet tells us that to be recognized as logic 0 a data input must be pulled down to 0.8V or less, and the current you have to sink could be as high as 1.6mA. Applying Ohm's Law, we get a maximum acceptable pull-down resistance of 0.8V / 0.0016A = 500 Ohms. 

The only problem with this method is that when you switch the resistor to +5V it will draw 5V / 500 Ohms = 10mA, so when all 4 buttons are operated the circuit will consume 40mA more than it needs to. If you don't mind this extra current draw then pull-down resistors are fine.