Well, that's not as interesting 
Anyway, you should start with each module separately. Get an LCD running and counting down on its own.
Then figure out the pressure sensor, or you could use a simple switch. I don't think you need a measurement of the pressure, just the information that a threshold is passed. A spring loaded switch would do the job as well, I suppose. Perhaps sitting surface of the chair could have a flap over its entire surface that is sitting on the switch. Something simple.