Finally, I was able to track it down to the fuel pump relay, which was making some chirping noise. First, I swapped it with another relay; but it made the same sound. Then I measured the fuel pump relay terminal voltage (coming from ECU); it varies from 3.5 up to 5 volts, which is supposed to be close to zero volts (ground) when the engine is running. So the fuel pump relay was never full closed.
As a temp solution, I removed the fuel pump relay and shortened the connection with a paper clip; I can hear the fuel pump running as soon as the car key is inserted. Now, my car can do cold start properly; but I have to find the real solution fast because this solution is not safe.
I suspect some ground connection was not tight (this car's engine was taken out for repair in June 2010 and no problem before that point). Thank goodness, I did not let the dealer change throttle body
Would someone help me with the electrical wiring diagram for 2002-2006 Camry? I need to locate the ground connections on this car. Thanks in advance.