The reason it is probably hydraulic related rather than booster related is that you said the pedal goes down a few inches and no further, but it does not stop the car. If there is air or no fluid, this is what will happen regardless of boost. It sounds like you are feeling the pedal mechanically bottomed out.
It only costs a few dollars for a quart of brake fluid. Flush THOROUGHLY with fresh brake fluid and then assess the system. The flushing will be a good thing to do even if you end up rebuilding the hydraulics.
You are most likely correct in paying your attention to the m/c first. Look at all the wheels and cylinders and see if there is fluid anywhere. If not, then the m/c is almost certainly the problem.
Henceforth, flushing the entire brake system with a whole quart of fresh fluid once a year will virtually eliminate these problems from occurring.