There is no such thing as a valve pump! The pump is the part mounted on the tractor if external has two lines to it. One the incoming oil and the other the outgoing oil. The valve (control valve) is the chunk of iron to which the handles are attached, and has the inlet port (usually marked in) which is also usually on the relief valve side. The opposite side is the Outlet (usually marked out, but also may be marked byd (Power beyond) The on the top on bottom top or bottom you have 4 work ports, two of which go to the main lift cylinders and two go to the dump cylinders. These ports give you double acting hydraulics or raise and lower and curl and dump. The levers you move are connected to spools that when moved direct the oil under pressure to the correct port. If these spools get off center due to a broken centering spring or something prevent their full travel it will cause a restriction and cause you problem. But that may not be your problem. If the coupler spring gets weak oil flow can cause the poppet to move and close the coupler to oil flow. Or a hose could be deteriorating internally and a piece of rubber could be blocking a fitting.
Most systems when a loader is added take a source of oil spilt it off send it to the loader valve and then either send it on to the s point hitch, hoe or other auxiliary valve. Not the best way but it will work. Why not the best way? This set up pressurizes the loader control valve and puts pressure on the sealing o rings. The correct way is to use the power beyond adapter and run that to the three point hitch etc. BUT then the loader control valve needs a separate return line to sump.
If your tractor does not use this pump to feed the three point hitch the the return hose can be return to sump and there would be no need for a power beyond.
Without power beyond
Hydraulics Systems Diagrams and Formulas for a front end loader, winch, logsplitter, and other useful formulas
crossmfg.com
A power beyond valve explained
Sleeve Assembly Part Numbers: BA 1V0208 3/4" NPTF BA 1V0209 7/8-14 SAE BA 1V0249 1 1/6-12 SAE SA/AD 1V2566 7/8-14 SAE
crossmfg.com
Also note most good loader valve will have load checks. A load check is a one way valve that will open only when the system pressure is higher than the trapped pressure in the cylinders. Without a load check the loader will drop slightly before raising.
If I were trouble shooting your tractor I would 1. be sure the valve spools are centering. 2 remove the inlet line at the valve return it to the tank/sump or the source of the hydraulic oil and test. If the return goes back to the tank/sump hook the inlet and return line together and test. 3 Unless the pump was added for the loader it had to flow to something else that had a relief valve in it, so even hooking those lines together should prove or disprove the loader valve. And may indicate a problem on down the line.
Remember the loader relief valve uses the return from the valve to relieve the excess pressure.
One more pointer if the lines are hoses any the are pressurized will visibly move as the pressure builds, and the component that is restricting the oil will get hot.
Good luck in figuring out your issue.