This is an updated post, but with some new and same problems. New problems are at the bottom. 

I have a 2001 Hyundai Accent GS with around 147,000 miles on it. Transmission is brand new 2019. Engine is stock engine. My brake pedal is very spongy and does not allow for emergency braking in hard stop scenarios and is not safe for the road at the moment. We have replaced the following parts with OEM and proper standard parts. 1.6 Liter 4 Cylinder engine.

Master cylinder & booster(OEM Part) dealership part $600

Calipers (calipers have flex to them) (Non OEM Part)

Pads (brake pads still have no bite during hard stops according to shop I had it tested at) (Non OEM Part)

We have had the rotors milled and they are still close to brand new on the thickness scales. (Non OEM Part)

Lines have been bleaded more than 12 times in total so far. Took it to a shop and they said the lines are more than perfectly clean. The guy said he has never seen cleaner lines. When he talked to me. 

New drums were put on the back wheels a couple months ago.  One is warped a little. (Non OEM Part)

Shop had adjusted rear brake shoes and bleed system with only minimal improvement. May have contamination in brake line, but the shop couldn't tell because we had already bleed them 3 times before. 

That's it for that. 

What happens before I start the car is I will get in and before I even put my key in the ignition I can pump the brakes and they become harder but remain sort of bouncy with a bouncy feeling. Then when the engine is turned on, the pedal loses all pressure. I can push it all the way to the floor and it has very minimal braking power. It'll stop the car slowly at 15 or 20 mph. But will never lock up like it was doing before and is supposed to. The dealership doesn't seem to know what's wrong with the car and my dad doesn't either. We are kinda at a loss for what could be wrong with the car. I can't seem to find the problem or solution on the internet as it seem to be a problem that not many have had. If ever...

After going to the dealership to get the Master Cylinder and Booster put on my car now does have a check engine light on but that hasn't effected anything that I know of yet. 

Any ideas on what could possibly be wrong with the car is very appreciated. Both my dad and the dealership are at a loss for words. And the mechanics I have gone to seem to not know what's going on either. 

New problems: 

P0300 code multiple Cylinder misfires detected 

P0303 code Cylinder 3 misfiring detected

P0302 code Cylinder 2 misfiring detected 

Alternator was bad, we went to a parts place like the puck and pull and got an alternator and the crank shift for the belt. Had the alternator tested and it was good. The old one was tested and was bad. 

Code P0722 speed sensor. We replaced the speed sensor on the transmission and the check engine light was still on. Though the 722 code no longer was read.

We had a P0304 for Cylinder 4 misfiring detected, but I had plugged the reader in and still have it in. The P0304 code is no longer there. 

I turned the engine on for 5 minutes and still have it running at about 15 minutes. The check engine light had cleared after about 10 minutes of running. 

Could the speed sensor code trigger the code for Cylinder 4 to be misfiring? And was the check engine light possibly on because of the alternator being bad or because of the misfiring or because of the speed sensor? Could it be all of the above?

I'm trying to pinpoint the cause so I can know what to tell my dad. I am replacing the EVAP canister right now as it is clogged. 

Again any and all opinions and information is welcome. Brakes are still the same as before. 

Something new I noticed is that when I press the brake pedal the RPMs do NOT visibly change, but the sound out of the exhaust changes. Don't know if that is me hearing the changes in the RPM or if that is caused by something else. Just something I noticed. When I press the pedal down it seems to stop outputting exhaust for a split second. It is very quick. Then once the pedal is down it resumes its normal sound. I do know that when the brakes were good and normal the exhaust never made that change in sound in the exhaust. So maybe this is something?