When i push down on the brake pedal air leaks out around the rod and the pedal goes to the floor.

no-- it is a lack of fluid in the master cylinder or air in the brake system
a power booster only assists the brake action and the pedal push rod goes through it into the master cylinder
check for leaks in the system , refill the brake reservoir and bleed the brake system
it may be a failed master cylinder rubbers

Hi Kevin:
What kind of vehicle is this?
Are you describing vacuum over hydraulic brakes?
It sounds as if the diaphragm in the booster may be torn, cracked, or otherwise compromised.
Brake pedal pressure when not running would be hydraulic system pressure only. If the brake pedal goes to the floor when the engine is running, you have a SERIOUS safety issue. Try to see where the extreme movement is happening. There may be parts that need replacement. Definitely repair before using.

play is defined as the distance the pedal travels down before the solid resistance is felt. If it goes down more than about 2 inches then re-bleed the brakes starting at the longest line first. If it is free pedal ( distance from initial movement to when the pedal rod touches the piston this should be around 1" measured from the floor to the pedal . It is adjustable at the end of the rush rod connected to the pedal.

Check for leaks around calipers....front and rear. Sucking in air somewhere...

when you push pedal hard & pedal goes to floor does brake light come on?
assuming brake fluid leval is ok & didnt run empty have you checked for a leak?
pulling all wheels & inspecting brakes,cylinders, calipers,& lines for leaks.
does the pedal pump up & feel ok with engine running?if so there is air in the system
if it does'nt change the way the pedal feels & no leaks are found & brake linings are ok & adjusted
properly than your master cylinder is leaking internally & needs to be replaced

If the pedal goes all the way to the floor you have air in your lines somewhere. If the pedal is soft and spongy then there is air in the lines. Start checking around the inside of your tires, and up near your Brake Booster and Master Cylinder

best place to start is looking for a leak in the system especially on corroded brake lines. fill master cylinder with fluid and have assistant gently push on brake pedal. check all fittings and lines for leaks. look carefully around gas tank as lines snake in front of tank above heat shield and are impossible to see without removing tank but leak will drip down at some point.

chances are the seal inside the master cylinder is blown (check for leaks before buying bits......)

YOU HAVE A BAD MASTER CYLINDER
HAVE IT REPLACED AHD YOU PROBLEM WILL GO AWAY

The brake assist is bad. Its located on the firewall. The brake master cylinder bolts to it. The rod comes from it to the brake pedal