Hi @wheeljack ,
It seems as though the speed controller may be defective. (the speed selector control switch and associated components)
How old is the mixer?
Hamilton Beach give a 1 year limited warranty on the product.
You could try contacting them, to see if they have spare parts or offer a repair service. A quick search online didn't find any relevant spare parts.
If your mixer is more than 1 year old and you decide to contact them regarding your problem I would express your disappointment to them that a quality product such as theirs failed so soon. Give them a chance to offer something for your disappointment ;-)