The black dust is often seen on PCB's, its not the cause of your problem.
Your initial description of the fault is a little unclear.
When you say it fills then stops then fills again does the water level appear to be coming to high up the door glass?
Its possible your outlet pipe plumbing could be at fault. It should go into a standpipe or connect to a sink waste that is well above the door of the machine.
If the outlet pipe is too low then it will be draining out as it is filling. Sometimes this can happen to a machine that has worked perfectly for a while. If the standpipe or the outlet hose is not secured it can drop down below the correct level.
I would be interested to know how you checked the heater was working
That which can be asserted without evidence, can be dismissed without evidence.