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So first, you can't blow backwards into the drain hose because there is a backflow preventer right where the hose connects to the pump below the tub. If you think the hose is clogged, you'd need to disconnect the hose below the tub and blow through it the other direction to make sure it's clear.
But since you just moved into the house, there is a good chance that the garbage disposal may be new and not adapted properly. There is a knock out plug inside the receptacle where the drain hose connects to the garbage disposal since not everyone connects to the disposal. Stick a flat head screwdriver into the receptacle and see if there is a plastic wall stopping you from sticking it through the receptacle and into the disposal. If so, then use a hammer and flat head screwdriver to knock the false wall out. Unplug the disposal and then reach down in and pull the plug out you just knocked out and you should be good to go again.
Now if that isn't your issue, then the hose itself would be clogged. You'd need to disconnect the hose from below the dishwasher and try to clean it out or make sure the area right where the hose connects isn't jammed up--those are the only places it will clog.
On this dishwasher, the motor just reverses to drain as opposed to washing. So the first thing you want to do is put the dishwasher on drain and see if the motor is running. If not you could have a bad control board. Otherwise if there is no disposal and the motor is running, you'll need to remove the drain hose and blow through it to make sure it's clear. If it's clear, then there is a blockage right at where the hose connects. You do not access the drain from inside the tub.
Hello again. I'm just following up because I haven't heard back from you and I see this question is still open. Is there anything else I can help you with?