It seems like your I3 state is working backwards. With a 2X4 I received two weeks ago, using 10K pullup resisters between +5V and I3 and I4, both inputs show OFF. Connecting each input to GRD turned the inputs ON. Perhaps such a large pullup resister value puts the + voltage in a range that is very close to the transistion between ON & OFF but a solid GND through the closed switchs put my I3 & I4 inputs in a solid ON condition. The Quick-Start Guide does indicate a 0 volt condition (GND) should put the input in the ON state.
Is it possible that the open/close state of your switch is opposite to what you think it is? If so then try smaller pullup resisters to put the pullup voltage closer to +5V.