Checkboard,
I think we need to be a bit careful here.
If either of the pipes become partly blocked it will reduce the rate at which changes in pressure are detected by the instruments and ADC. But this does not mean that the full pressurs will never be detected.
If for example the pitot pipe becomes blocked, the ASI will be slow in detecting speed changes, but will give an accurate reading after a brief period in any given flight condition.
The effect will be similar if the static pipe becomes partly blocked. You will eventually get accurate indications of speed and altitude but the repsonse rates will be lower. Indications of rate of change will also be incorrect.
So a partly blocked pitot pipe will give:
Under indication of speed when accelerating or descending.
Over indication of speed when decelerating or climbing.
Correct indication of speed in constant speed level flight
And a partly blocked static pipe will give:
Over idication of speed and altitude when climbing.
Under indication of speed and altitude when descending.
Under indication of rates of climb and descent.
Correct indications of speed and altitude in constant speed level flight.
I suspect there are some other but cannot think of them at the moment!!!