With cars this old, the calipers tend to seize up or start sticking.
If you suspect the master cylinder, put the calipers back on and start the engine; then press the brakes and see how they feel. If its stiff, then you are making good pressure; if it slowly loses pressure over time you may have an internal master cylinder leak. Also check the brake fluid level, and visually look around the master cylinder for brake fluid leaks. If all is good, the caliper is most likely the culprit. I'd check the condition of the brakes at all 4 wheels before coming to any conclusions, it could be time to replace the pads and rotors and/or rear brake components like brake shoes and wheel cylinders.
Not the same car, but a friend of mine has an early 2000s Neon where the brake material on the rear shoes broke off of the shoe and jammed against the drums, completely locking his rear wheels. And I have a 94 Toyota Van with pretty low miles, the front left caliper seized on the second piston and drug the brake pad; could really smell the cooked pads and probably warped the rotor. It happens, but brakes are cheap and easy to do.