Solder joint used between copper wires and a button switch is behaving strangely. I don't think it's a cold joint
The problem here is there is no input to the NOR gates when the switch is open.

Basically, when you have an undriven logic input, the input is undefined. This means it could be high, it could be low, it could toggle randomly as a function of local electrical fields. This is colloquially called a floating input, because the voltage on the input "floats" around as a function of local electromagnetic influences.

Since it seems like you want the inputs to be high except when the switch is closed, you need to add a resistor between the inputs and the positive rail, to pull the inputs into a known state when the switch is open. A few KΩ should be fine.



Ok, more troubleshooting. First, I'd stick pull-ups in there anyways. Relying on the internal behaviour of the input buffer makes me uncomfortable.

Next, rather then just wondering if your solder joints are bad, just measure them! You should see ~Vcc at the input from the switch when the switch is open, and ~Gnd when it's closed. This should be quite easy to test, even with a cheap multimeter.