The Vinik AV system has two control panels. One is located on the left wall of the booth (pictured below), and the other is stage right near the audio rack. Press the button under "ON." You should see the projector and screen lowered into place and the projector should be on. This can take several minutes.
If this doesn't happen automatically, use the "proj lift up", "proj lift down", "screen up", and "screen down" buttons to raise/lower the projector and screen.