In short, if the pitot becomes blocked the airspeed indicator will act like an altimeter.
If a single static source becomes blocked, the pressure instruments readings will become erratic and unreliable in a slip or turbulence.
If both static sources becomes blocked the altimeter will show whatever it was showing before the blockage occurred, vertical speed indicator will show zero and airspeed will over read during descent and under read during climb.
The quickest way to determine if you have an instrument failure or a static source blockage is to check the vertical speed indicator, if it still works, its an instrument error. If not its a static source problem and airspeed is unreliable.
Be aware that on more advanced planes the vertical speed might be coming from an inertial unit instead of pressure driven 
.