Inside view of lml of sony ex3 - Sony VPL-EX1 Multimedia Projector

SOURCE: Sony VPL-EX3 "Lamp cover problem", it wont switch

There is a small switch that detects when the lamp cover is securely tightened down, so that it protects the user from the high voltages, hot surfaces, excessive bright light in the eyes, and damage to the face if the lamp implodes due to old age and overuse.
so check if the switch operates when a toothpick is pushed up and down in the cavity.This model suffers this problem when the cover is slightly warped with old age.
so put a strip of folded paper between the cover plastic protusion that actuates the switch and the switch and secure the cover and see if this is all that is needed to activate the switch properly.

if it now works, you can try putting a small drop of silastic on the cover protusion and wait till it sets over several hours in order to lengthen it slightly so that it reaches the switch properly