lets go back and start over and try to figure a few things out......
forget about what the last dishwasher did, that may have had a different programming or time frame to allow filling.......
starting with this new one, how long is the time frame it is allowing for that valve to be open to allow it to fill?....my KitchenAid TT only allows 60 seconds..
second.....household water pressure.....with the aerator removed, turn on the hot water.....can it fill a gallon of water in roughly around 30 seconds?...I have extremely high water pressure, so I cant exactly give you a comparison...
next your going to want to check the water valve and supply hose to make sure you are getting proper flow and pressure to the machine.....
wondering, if you were to allow the machine to fill, then stop it, cancel and re-start the cycle....will it drain first, or allow it to add more water and continue on?....
I am just wondering if that machine is just not good for your particular application.....and that it may not be a machine error at all.....
lets just try to go step by step...and rule out a few things....obviously it runs fine if you add more water.....
most machines obviously are time fill, the overflow/pressure switch is only there for cases like mine, where it fills faster than the time allowed, and so it doesn't overflow....
lets see if we can get to the bottom of this......