The brake pedal going to the floor usually indicates that the master cylinder is leaking internally (bad cup seal). It could also be a leak somewhere in the system.
Your motor bogging down when the brakes are applied could mean that the vacuum booster is leaking, but could be something else. Compare the brake effectiveness with the engine off with engine on. If there isn't much difference, a leaking vacuum diaphragm in the booster could be the issue. With the engine off, pump the pedal till it gets firm, then hold it and start the engine, if the pedal goes toward the floor (but not all the way down) then the booster is working as it should.
