Was it replaced with a new one or a remanufactured one? I have seen problems with remaunufactured units as the core is not adequetley rebuilt.
Yes, my Dodge Caravan has brakes.
Brake cylinder repair is that wheel cylinder that holds the oil to keep your brakes running smooth on your back brakes. If you don't repair those you will mess up your rotors and your rims.
You need to "bleed" the brakes at each wheel. R
Master cylinder
A master cylinder should be replaced when it can no longer provide the pressure needed for the brakes to operate. You can tell it is failing when the pedal becomes soft.
The Slave Cylinder and the Master Cylinder control totally different systems. The Slave has to do with the clutch, and the Master has to do with the brakes. They have nothing in common.
The best way to tell when you need brakes is by squeaking, when the brakes are rubbing against the metal, when your brake pedal goes all the way to the floor and when you are running out of break fluid.
If the rear wheel brakes are locking up on a vehicle they should be thoroughly checked. The master cylinder may need to be replaced on the car.
You need to bleed the brakes.
Either your emergency brake is hanging up or your wheel cylinder is leaking fluid and needs replaced if drum brakes and if disc brakes the caliper could be bad.
The issue here sounds like it's the master cylinder failing. It is not retaining pressure when the engine is running. The reason they feel fine when the engine is not running is because the failing master cylinder is not getting power, and in essence is being bypassed.
I would suspect the Master Cylinder if defective. I had the same problem with my 1978. I replaced the combination valve and it solved the problem after bleeding.