> No, the internal pullups are off

Do you explicitly turn them off ?

> I have removed the switches and associated pull-ups from
> the circuit and replaced them with just 4.7k resistors from
> each pin to ground, and the same problem occurs

That sounds like a clue. How can a pin read as '1' when it
has never been set to '1', internally or externally ? Could
this be a faulty IC ? If the set-up is as simple as you say then
what you're seeing doesn't make sense (but you already
knew that ;-))

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