Can I use Liquid Plumber to clear the drain?

No don't do that ! take the plate off of the bottom of the dish washer, you will see the drain line, remove this line and the hard line screws out as well.( you will need a pair of pliers to do this ). Clear debris from the hard line and re-install hard line as well as drain line.
Before attempting this though make sure to remove the water from inside the dishwasher either with a shop vac or a cup, you will also have to have a small pan ready to catch the water with when removing the drain line.