Four things come to mind as long as u are sure the tub is full and the pump is running.
One: debris like some plastic, broken glass or grease or food buildup is preventing water from entering the pump inlet. No water return = No wash, poor water return = poor wash.
Two: the impeller is broken or loose on the pump shaft and is not turning when the motor is running. No impeller motion = no water flow = No wash.
If the tub empties and the pump sounds "normal" then the impeller is likely OK.
Three: excessive clearance or blocked motion of the lower wash arm. Clearance would be due to a broken or missing shim/arm seal under the washer arm. Water would squirt out from under the wash arm and not wash dishes. Blocked motion could be due to something in the bottom of the tub like a big utensil or the dishrack not setting on the rails properly thereby blocking motion of the wash arm.
Four: If this model has a directional water squirter on the top of the center of the lower wash arm then look to be sure all of the parts are there. If parts were missing it could create a big hole to pump water out. If it is missing parts, then the sound inside the dishwasher would be like a water from a hose hitting a wall, except that the pump would sound normal then spin very fast then sound normal. This is due to almost all the water in the tub being quickly pumped straight up into the air then the pump sucks air until the water falls down and then the pump sends the water back into the air again.
Hope this helps.

Let the unit fill with water.
Then open the door and check the level.
Most units should fill to just under the heating element.
If it is low add a couple quartz of hot water.
Let the cycle finish.
If it now washes good, odds are high that the filter screen on the input side of the water valve is partially clogged.

Remove the sump cover.
It is the cover on the tub floor just behind the spray arms.
Take note of how the inner baffle is installed. Put it in wrong when you reassemble it and the chopper will eat it up.
Check in the sump for debris (broken glass etc.). Also for anything that is wrapped around the chopper.

It didn't fill at all much. I had to put about 6 quarts of water in it, and there are suds in the water!

I would remove the water inlet valve and check the filter screen on it's input side. There is a good chance that it is partially clogged.
Do not remove it as it is there to keep crud out of the valve which could hold the valve open and cause a flood.
Also a good idea to drain some water out of your hot water tank, Crud accumulates here and eventually will contaminate your plumbing. This also make the tank run more efficiently.

If the screen is clean then odds are high that the valve needs replacing.

You may have another problem but this definitely needs fixing first.

Also, there were suds in the water. I had put about a teaspoon in the dispenser a few days ago. It never washed out, so it was still in the dispenser, but hadn't budged from it's little home.
Not sure what the above means, please clarify.
Are you saying that you put a teaspoon of standard dish soap into the rinse aid dispenser?

Would that have anything to do with the water intake line too?
If the suds are thick enough to lift the float which controls the water overflow switch then yes but I doubt this will be the case.

The water overflow protection switch is under the tub behind the kick plate, usually on the left hand side. You will probably see a shaft coming down from the tub, this holds a switch closed which provides power to the water valve.

If the float in the machine rises (lets say if the unit overfills with water as an example), the shaft rises, the switch deactivates and power is turned off to the water valve.