What's failed?

The needle that doesn't move

The attitude indicator shows a climbing left turn, and the heading indicator, turn coordinator, altimeter and VSI all agree. The power is set to full and the altimeter shows a rapid climb. The airspeed indicator sits fixed in the yellow arc, which is odd for a climb, and it doesn't budge. A real airspeed needle wanders a few knots through pitch changes like these.

The gauge, not the plumbing

The airspeed indicator is one gauge fed by two lines, the pitot tube and the static port. A blocked pitot doesn't freeze the needle in a climb: with the inlet blocked and the drain open it reads zero, and with both blocked it acts like an altimeter and reads higher as you climb. A blocked static port would freeze the altimeter and hold the VSI at zero, and both are moving. So the plumbing is working, and the gauge itself has failed.

One failure, not five

The VSI does fluctuate, but it moves right along with the altimeter. When one instrument disagrees with five others, one failure is far more likely than five.