Using a 74HC590

_MRC (pin 9) to GND

Uh, _MRC is an 'active low' signal so you are doing a Master Reset of the Counter all the time? Try a pull-up on that pin.

_OE (not connected)

If you don't pull this low you won't see any outputs. Try holding that one low.

You also don't mention _CE (Counter Enable). You should tie that low.

I don't know if it is true of 74HC chips (High-power CMOS?) but for most CMOS chips you have to provide inputs for every input pin. If you let the input float it MAY cause an internal short and fry the chip.