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As you're trying to piece this puzzle together, let me add some things you may not have considered...
Virtually all of our training in pitot/static failure modes is in unpressurized aircraft. Even the recurrent training at Flight Safety & RTC does not cover the variables that a pressurized system introduces.
How does pressurization complicate this? If you have a static leak inside the pressurized vessel, some very strange things happen.
For instance, upon takeoff, adding power will lower the indicated airspeed (i.e. peg it at zero). It also shows a descent on the VSI and altimeter. Pulling back the power has the opposite affect - suddenly the airspeed comes alive and the apparent descent ceases.
At altitude, if the static reference opens to the cabin air, it would suddenly increase by the dPSI (i.e. 3.35") which would cause the airspeed to peg at 0. You would also notice both the VSI and altimeter showing a rapid descent.
While there are lots of pitot static connections inside the pressurized vessel, I believe the most likely source of a leak would be the alternate static switch/valve.
In your case the problem was intermittent - and if it was unaccompanied by strange VSI and altimeter behavior, then I would guess that it was a blocked pitot tube. In any case, the first thing to do in this situation would be to try the alternate air to see what (if any) effect it has on the problem.
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