The dishwasher fills by time only.
The float switch is only a safety so it does not over fill.
Ok if the unit is filling and the drain pump is running ,that has to mean that a relay on the control board is stuck to energized the drain pump in this sequence of a cycle.
Which means the entire control board will need to be replaced.
Because the manufacturer does not sell individual components of the board only the entire board.
The link below is to the part you will need from a highly recommended company rated A+ with the Better Business Bureau.
They offer a 100% money back guarantee, EVEN ON INSTALLED ELECTRICAL PARTS, for an entire year!
They are the only company to allow returns on installed parts for a refund and offer a FULL ONE YEAR WARRANTY!
This link also has a video showing the replacement of the part.
If you have any questions just reply back.