The water temperature switch is mounted right on the console along with the washer timer and the dryer timer!
Here is a parts break down it is shown as item #10
Ok On the water valve your purple is shown as blue ,which when faded does look purple.
and if your getting voltage on the blue /purple to ground ,but not to white you have lost neutral to the water inlet valve assembly.
And as shown on the wire diagram the white /neutral comes off the fuse from the fuse it comes off the pressure switch on the white contact #15-E then thru the pressure switch contact #34 comes out on contact #3C yellow then to the level selector #C into the level switch and out on contact #7 as a gray wire .
So either the fuse is bad , even thou you have tested it , or either one of the contact in either the pressure switch or the level selector are bad or you do not have a neutral coming from the terminal block or from the outlet.
That is why it is called a floating neutral . because when not under a load it is there when under a load as if something is being powered it goes away .
The something being powered in this case is the water inlet valves.