From what you are describing, it sounds like the lamp may have overheated and caused the thermal switch above the lamp area to pop. When that happens it shuts off the mains AC power to the projector's power supply.
What model projector do you have?
I would remove the lamp and see if the connector has burnt up. IF the lamp is difficult to remove, you may have to cut the wires leading to the lamps plug, but of course only do that as a last resort.
I have emailed a friend in Singapore to see if they can help, and they asked me for the model #.
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