Without the engine running, with power brakes, it will "feel" as though you have a full pedal, while actually you don't.

Try this :
Find an open non public area.
get up to about 20 MPH, put it in neutral, switch off the engine and see if you REALLY have any brakes.
My bet is you will coast for a while until you start the engine back up.

If I were you, I'd do this :
1. rebuild or replace the master cylinder.
2. flush out all the old brake fluid with a complete bleeding job.