You are on the right track, if the lamp is not lighting bright enough it could do this exact thing, the three tries is standard on RCA products, called the 3 strikes and your out---set will try 3 times to make it on and then shut down.
The color wheel while possible usually makes a high pitched fan like sound and with lamp out you should be able to see it to know if missing parts of the wheel or shattered.
typical color wheel.
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