On the Dash 8-300 the APU (Auxiliary power unit) can only be used on ground for heating and electricity. It is switched off before or shortly after the engines are started. An inoperative APU on this airplane has no affect on the saftety of the flight, some don't even have one as it weighs about 500-600 lbs (leaves the basic weight of the airplane lighter - thus less fuel consumption or more payload/passengers).
As far as I have heard it is pretty common on the Dash 8-400 to have inop APUs in winter by the way the airinlet is designed. It's pretty much on top of the fuselage so if it there is snow on the plane and it melts/gets deiced it often gobbles up a big amount of water - thus killing the APU.
Hope that helps
- no comments on the pressurization though as I don't know what really happened.