Low voltage form a NAND logic gate then the state is high
You description of voltage measurement and state of inputs is completely unclear, but I suppose the main problem is that the ICs you are using have open collector outputs. It is (maybe) intended given you want to shift voltage level, but in any case you need pull-up resistor at the output to make such gate to work.

But there is not much point in using an open collector output for level-shifting purposes when you are powering the IC from 5V anyway. And in lot of situations (depending on your particular use-case) the push-pull output will perform much better than pull-up resistor.

If you want to shift voltage from 3.3 V to 5 V using the logic gate, go for the standard push-pull output, power the gate with 5V supply and check if the input levels match IO output voltage of your MCU (TTL-compatible versions of logic gate are better in terms of guaranteed high level voltage range for such purposes).