You seem to have two separate problems. The soap on the dishes not being rinsed off and the black residue left behind as well.
The soap being left behind is most likely a circulation or drain problem. The water should be up to and near the element. Run a rinse only cycle to check the water level. After if runs for a few minutes check the level again to make sure it is the same level. If the drain is not routed correctly then the water might siphon out of the dishwasher while it is running.
Make sure there is not an excessive amount of suds in the washer. Extreme sudsy water can prevent a complete drain out.
The black residue might be a little more difficult to figure out.
I suspect the back residue is mildew and if this is the case then most likely the dishwasher water heating system is not working.
One way to check this is at the end of a wash cycle when the door is open a lot of steam should exit when the door is open. No steam would indicate a water heat problem.
No water heat would indicate a problem with the water heating system. The problem might be with the timer, hi-limit thermostat or element.
I hope this information is helpful to you but I will most likely need a few more details to give you a more specific answer.