[Murco]

Diagnosis -
If you currently have a brake issue here is the order of diagnosis, and this applies almost universally in brake repair...
The first thing to do is make sure the bottom-end is good. The calipers (and wheel cylinders) aren't leaking, frozen, or full of sediment. If they check out the next thing to verify is that the fluid hoses and lines are in good shape. No bulges or kinks in the hoses (if they have inner wall damage you'll usually have a significant pull under braking), no crimps or breaks in the hard-lines, and no leaks.
If all the lower components check-out flush the system and have someone (a dealer if necessary) cycle the fluid out of the ABS pump (if so equipped) to make certain you have no air in the system - which will give you the same indications you asked about.
If after these have all been checked, the fluid fully flushed, and you still have the same symptoms check your booster and the vacuum going to it. If you have access to a vacuum gauge check the booster vacuum, it should read no less than 14 inches at steady idle. If lower than that check the hose and fittings for cracks or leaks. You can use a can of starter fluid, just as you would a manifold or carb leak, running a spray along the length of the line listening for an RPM rise.
If you have good vacuum and feeder hose/fittings then have someone push the brakes with the engine idling, listen for the sound of a consistent air leak while they hold the pedal down - it's obvious when you hear it, a "whooshing" sound that continues while the pedal is held down.
As I said earlier, diagnostics starts at the bottom and you need to work your way up in the system. If you've followed these steps in order (which even if having the flushing done at a dealership should be well under $100 so far) and still have a weak pedal it is likely that the master cylinder is done. Now let's make certain!
Remove the master cylinder, using proper fitting wrenches for the lines, drain it, and clamp it securely in a bench vise. Put bleeding caps with tubes on the outlets (your local auto parts store should have some), refill the reservoir, and slowly push and release the plunger at the back using a screwdriver with the bleeder hoses in the fluid reservoir. Continue the push and release until the bubbles stop coming out of the hoses so you'll know the master is air-free, then remove and replace the bleeder cap with a block-off cap on the rear outlet and attempt to push the plunger again. If it's solid and won't move the primary side is good. Return the bleeder cap and hose to the rear and place the block-off cap on the front outlet and try to push the plunger again, You should be able to move it a little but maybe only a half stroke compared to when you were bleeding both outlets.
If you should go through these steps and haven't found an issue feel free to PM me and we'll start really digging.

As an example of how fun this stuff can be to diagnose I'll use my 1992 Lexus SC400 with ABS and Traction Control. It had a pedal pressure issue when I bought it (really cheap) except mine was constant. The car had 260k miles on it but was meticulously maintained with records going back to day one and looked perfect, like a new car. As with any used car I'd buy I immediately rebuilt the calipers, installed new pads and rotors, inspected the line and hoses, flushed the system, got a good pedal and felt I'd resolved the issue but expected more since the car had been maintained by the dealer all it's life and they would (hopefully) have done the same thing... After driving it for a few days I noticed the pedal started getting spongy again, a quick reverse bleed had bubbles in the master cylinder and looking through the lower hoses and lines again yielded nothing. In fact the hoses were recently replaced. I checked the tightness of the hose ends, all good. I checked the 16 line connections on the ABS module and found one that had a tiny amount of fluid on the outside, like the amount that you would leave if you bumped it with a wet hand! It was the line that provided fluid to the ABS pumps from the master cylinder and air was getting drawn into the system there. The 1992 traction control system was one of the first and, as you'd expect, it was convoluted and complex but it ended up being a $49 hose that got me a high mileage but nearly perfect Lexus for $800! I did contact the dealer afterward for info on the car and the service writer told me they had diagnosed a bad ABS unit and quoted the previous owner $3600 for a replacement, so then I knew why I got it so cheap. That was 18k miles ago and I still have a fully functioning brake, ABS, and Traction Control systems with no further troubles, although I can't imagine the original Master Cylinder lasting much longer!

After reading all of this, even if you don't do the repairs yourself, at least you have the knowledge to ask questions and sift-through any BS thrown at you and that's the whole point if this thread. I'm a brake geek (a geek in many ways) and trying to diagnose something without being there and doing all the things I'd do instinctively is tough so I won't pretend to be able to fix all issues with a brake system through forum posts. However, I am happy to provide all the expertise I have so that when you get into it yourself, or have it done elsewhere, you'll have the information you need to spend your time and money wisely.
Happy braking!