If the motherboard was designed in such a way, it would require at least one slot from each bank to be loaded. Laptop motherboards aren't standardized like most desktops, and that allows for OEMs to take creative liberty in their designs.
If that one 2GB card was defective, it would still fail to post with the other cards in. Again, it may just be a flawed design.
The maximum memory supported by your laptop's motherboard is 8GB DDR3 @ 1333Mhz, as per ASUS technical specifications. 32GB of RAM is not possible on this machine.