I'd try bleeding your brakes before you go ahead and play with the brake booster.
Unless you've already done all this stuff and know it's the brake booster. I ran into a problem like this not too long ago. Thought it was my brake master cylinder because I had the same pedal problem as you.
Through research, I came to conclude that the master cylinder or improper bleeding of the brakes cause the pedal to sag to the floor without applying brakes, and if it is a faulty brake booster then the pedal will not easily be pressed down... I could be completely wrong about the brake booster part. I did inquire about it, though, and I would recommend getting the same one you originally had (ie; ABS for an ABS car, non ABS for non ABS)
On a dual side note, there is a check valve in the brake booster line. I just installed a vacuum block in this line, but you might also want to check and confirm the valve is good, and that there are no leaks anywhere. Are you losing brake fluid? Did this problem come out of nowhere or did it happen after you messed around with something (brake pads, pretty much anything)...
Sorry I'm not more factual or decisive, but thought that maybe my background knowledge may help you out a bit! Good Luck!