Noisy transmission

Hi,
Got a small problem. I think it's transmission related. When the car accelerate with first gear, I hear very noticeable grinding/groaning sound from the engine compartment, even when the car accelarate very slowly. The sound is barely noticeable on 2nd,3rd,4th gears; and I could only hear it when I floor the gas pedal. When the car is sitting still, reving the engine doesn't make this sound. This has been going on for a few months.

Today, I notice something that makes me think the problem is transmission related. My car was parked on a hill. I disengaged the parking brake and the car rolled backward slightly and stopped because it was in Park. I started the car. The engine automatically reved to 1500 RPM as usually when it's cold. But this time, I hear the grinding/groaning sound, and it was quite loud. When I take the transmission out of park, the sound goes away. This was the first time I hear this sound with the car sitting still.

Any idea if the problem might be?

92 Integra Auto Transmission