I have a single shower valve with no identifiable mfr name.
no cold water comes out of the valve unless you turn the hot water tank valve off and open both spickets at the sink which shares the same supply pipes.
when you take the cover off the shower valve you can see a screw valve on each supply line feeding the shower valve. both of the screw valves are in the full open position.
If you turn the hot water tank back on the cold stops coming out of the shower head and is replaced with hot only.
I also removed the shower valve and it appears clean.
It sounds like a stuck pressure balancing spool. The method of repair depends on the make/model of the valve.
I would suggest posting a picture of the valve.
is the pressure balancing spool contained within the cartridge?
It depends on the make and model of the valve. Can you post a picture of it?