The three way valve (actually it is a 2-way) is in parallel with the solenoid. So the solenoid has no impact.
I find the theory that the three way valve is the problem not very likely. But it is easy to test as you can remove the pre-filter and see if fresh water comes out of the filter connector when you open the three way valve for fresh water.
My guess is either a clogged connection hose or stuck valves in the high pressure pump.
Take off the hose between the pump and the membranes and see if fresh water comes trough. If not the pump may be the problem. Next reconnect the hose and remove the brine (output) hose from the membranes. That is the high pressure hose on the other side. See if water comes out of the connection point. If so then the problem may be in the regulator at the console.