This happened to us a few months ago. First DH took the hose off from the back of the dishwasher We took it outside and ran water through it with the garden hose. DH also disconnected the u bend from under the sink and washed that out.
Not wishing to be sexist or anything, but it's not something I could have done by myself. DH knew which bits to disconnect. Turn the water off too!!
Could you ask the assisitance of a friend or neighbour?
It worked when we did this and saved us a fortune in call out fees for the engineer.
Do hope you manage to get it sorted.
Our got clogged because I'd forgotten to remove the paper label from a jam jar!
We don't have a garbage disposal thing. It was grease and a scrap of paper.