What will happen if I use an output 13.5V, 1100mA - Input 120V-60Hz 32W power supply to power an item needing output 16V,1000mA - Input 120V-60Hz 29W?

You run the risk of overheating the powersupply and or the computer. Dropping the voltage down could also wrek havoc on your primary systems making things impossible to recover.

Sounds like a laptop power supply. In that case your battery may not fully charge and possibly over heat. The life of your battery will be negatively affected.