[LazyPup]

We will need a bit more information here.
What make and model of washing machine?
You said the machine was recently moved, are you sure the water faucetts are turned on?
Some washing machine hoses or water valves have screens on the inlets. Check to see is you have screens and if they are perhaps clogged with debris.

Normally when a washing machine cycle is started the first function is to open the water valves for the fill cycle.

The timer motor is connected in series with the water fill valve and the timer should not advance to a motor run position until the tub is filled to the proper level.

When you see the water in the soap dispenser and subsequently pumping out, are you manually advancing the timer beyond the fill cycle?

In regards to the drain line. Washing machine drain lines are typically 1 1/2 or 2 inch lines which are to be run with a 1/4in per foot pitch. (1 inch fall in four foot run).

The pitch of the drain line should have no effect on the fill cycle of a washing machine.