Is this a coleman pump stand? If so, the thumbwheel you describe is a needle valve and those are compression type fittings.
You could indeed have the system gunked up and it would need cleaning out. I'd drain the tank and clean the filter and refill with a good strong solution of wax-like a red trip on a hydrominder.
A quick hack is to try to suck the gunk out of the lines. Have someone turn on the wax and pull the trigger on the gun in the affected bay . Starve the pump for water by slowly closing off the water supply valve until the pump gets noisy. This will create a vacuum on the chemical line and it may suck out the gunk. Just do that for a short period of time-15 seconds or so. If it starts working you'll see wax come out.
I remove the needle valves because most everyone runs them wide open anyway and replace them with standard fittings. Just one less thing to fool with.
You can use a wire coat hanger to clean gunk out of the poly lines or just replace them.
A final thing I've had to do is to disassemble the solenoid and shave the plunger seat with a
razor blade. Some products can make that seat swell and it will not open enough to provide flow.