PJ402D Viewsonic projector light comes on and shuts off after a fews seconds

Based on what you're describing, it sounds like a failure in the lamp ballast itself. The projector will probably need to be sent for service.

If you have a spare lamp, that would be the first thing to try. However, if it isn't that, it is likely the ballast.

Sounds like the ballast board for the lamp stopped working.

Hello,
If you are connecting the projector to the signal source via S-VIDEO cable this not uncommon. It usually happens when one of the connectors or the cable is broken. Try a new or different cable. If problem persists examine the connectors on both end of the cable and the one in the projector as well as the one in the signal source(pc, laptop etc) to see if there is a hardware fault. If all is good then the problem is internal with the S-VIDEO connector. In that case your other option is to use VGA.
Have a good day, hope this helps.

disconnect cable from the projector end. Then connect the free end of the cable to an LCD monitor to confirm that the video is coming out the laptop and out the same cable.

Then reconnect the projector.
press the source button until the video appears

Your Heat Sensor is probably faulty, try a replacement.

you need to hold function down and press something like F1 F2 F3 F4 maybe twice to clone the screen display and make sure your projector is on vga and there is a secure connection between your laptop and your projector.

As soon as you turn it on hold down the menu button until the lamp turns on.

Your lamp may well have died..

are there any leds on? if not, the power supply is shot. if there are leds on, the color and number of flashes will tell you the problem.

I had the same problem awhile back and looking around for an answer i found this.
http://recklessphilosophers.com/2008/05/02/home-theatre-for-63--dlp-pj-retrofit-for-7-bulb-instead-of-300.aspx