Pulling a dishwasher out isn't all that hard, just make sure to turn the water and power off. I'd then lay it on it's back and take off any hoses you can that have hose clamps and see if there is any obvious clog. Does it sound like the pump is running? I once had a tooth pick clog the pump impeller.
It's going to look something like this, so it isn't all that complicated.
Oh, also make sure the drain line to the sink is elevated properly.