Follow the light path and inspect carefully for dust or contamination. These pictures show the optical assembly upside down.

Light enters from the lamp on the right, facing the screen (on the left in this picture since it's upside down).

The light then passes through the colour wheel ...

... and into the collimator.

If dust or contamination has been sucked into the projector by the fan, it can deposit on and around the collimator, resulting in shadowy patches on the projected image.