Ok try removing the hose from the garbage disposal and put it in a large bucket higher than the water level in the dishwasher and drain it. It should empty out fairly quickly. If it does you might have a blockage at the disposal either where the hose attaches or the disposal itself. I find with mine that I usually have to run the disposal before the dishwasher to clear it of any debris or it backs up and when the dishwasher stops the dirty water drains back into the dishwasher. If it doesn't completely drain with the bucket then you have blockage inside the dishwasher and you need to disassemble down to the impeler to find it.
The garbage disposal is running fine, a nice "hum" when I run it and sink water goes right through.
When you say the "hose from the garbage disposal", do you mean the hose that goes from the dishwasher -> sink overflow thing, or from the sink overflow -> garbage disposal?
I don't have a "drain" button on my dishwasher, but I did remove the hose that goes from the washer to the overflow valve, and placed the hose lower then the dishwasher to create a siphon effect, and the water drained smooth and fast into the bucket.
I am thinking its a pumping problem, or something glogged internally deep inside the machine.