If the brake servo unit fails the brake pedal goes hard and a lot of pedal effort is required to stop the car. If the master cylinder is bad the pedal may travel to the floor, brake master cylinder may not be able to compress the brake fluid to generate brake fluid pressure. You may also have a brake fluid leak but it sounds like the car is unsafe to drive.
To check the master cylinder I often put line clamps on the brake flex lines to see if the pedal improves or put blanking plugs in the metal lines on the master cylinder to prove the cylinder is bad.
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