What does the pressure gage indicate when you use the 3pt? If you have good pressure, then the valve is faulty, perhaps the relief , or the piston seals are bad.
With a good pump, and valve, the pressure is determined by the load on the 3pt, and with enough load, the 3pt valve will relieve, and then you will know your relief pressure.
Did you say that you had no pressure to the remotes? Have you checked pump pressure yet?
If an upstream valve is leaking fluid, or the upstream valve is stuck, it will not pass enough fluid for the 3pt to work.
If your pump is good and working, then the hyd fluid is going somewhere. If all valves are in neutral, the fluid flows through all valves to the reservoir.
If the 3pt is starved for fluid, it won't work, if the 3pt valve is faulty, it may by-pass the fluid to the reservoir. or the pump is bad and can not develop pressure, or the 3pt piston seals are about gone.
When you put air to the 3pt cyl, did it hold air, or leak down rapidly.