How do you Test Polaroid projector lamp?

I'm assuming that you're talking about a LCD projection TV.

Since it's a Mercury vapor gas discharge lamp, it can't be tested with any type of continuity tester to see if the filament is burned out.

So let me ask you a couple of questions to help you make a determination.

1.) Does the "LAMP" light on the front of the set blink after the set's turned on? (Yes? Replace the lamp.)

2.) Does the TV come on and display a picture for a few minutes and then go out for a few before coming on again? (Yes? Replace the lamp.)

3.) Does the lamp not come on at all, but if you listen carefully, you hear three snapping sounds like high voltage arcing somewhere near the lamp's installation door? (Yes? Replace the lamp.)

4.) Are you able to remove the lamp and look at it? Is it shattered inside? (Yes? replace the lamp.)

5.) Are you able to remove the lamp and look at it? Does it have a rather large bulge at the base of the tube? (Yes? Replace the lamp.)

6.) Can you borrow a a lamp of the same type from a friend that has the same type of TV and it works OK? (Yes? Replace the lamp.)

Other reasons for a lamp not coming on:

1.) The lamp door switch isn't properly closed (safety switch) usually from removing the cover and not properly replacing it.

2.) The lamps' ballast unit has gone bad. (Especially if the door switch is properly in place and you don't hear the three clicking noises as it tries to ignite the lamp).

There's other possible causes, but in most cases it's either the lamp itself or the ballast.