Definitely sounds like a master cylinder. If it's just one leaking line, you would have at least some brake pressure, albeit not necessarily enough to drive safely.
Though not a licensed mechanic, I have worked on hundreds of cars over the years, and I have to warn you that tearing into the brake system can have a domino effect, especially if it's an older car with corroded lines.
Case in point, my 2010 Ram pickup truck. A couple of years ago, one of the soft lines in the front had an internal collapse that was causing the wheel to lock up. Replacing a flex line is usually not a big deal, but the collapse caused overpressurization in the ABS control module, so that started leaking. Being a work truck that just needs to, well, work, I didn't spend the several hundred dollars for a new module. I bypassed it using about 20 bucks worth of parts. Even had I replaced the module, just pulling the lines off of it caused ruptures in a couple of the solid lines. To make a long story short, I thought I was replacing just one soft line, and ended up doing nearly the entire truck.
I hope this does not happen to you. Good luck.