The difference you describe with engine off/on is the servo effect (not saying you are wrong about the brakes, but what you describe when stationary sounds normal-ish). If you pump enough times with engine off, the vacuum in the servo is exhausted and the pedal goes hard because you now have no servo (or power boost if you're American) assistance to the brakes. Start the engine and you get new vacuum (via pump if diesel as they don't make much vac), so the pedal is lighter (softer).
It does sound as if you have an issue there all the same - I had my rear discs and pads done a while back and whilst they weren't any better feeling, they weren't any worse.