Chrysler Neon transmission noise

Hi all,
I have a Chrysler Neon 2000. A few seconds after starting the engine (gearshift in neutral) I hear a friction noise coming from the transmission. If I press the clutch pedal it stops. After the engine gets warmer I don't hear it any more.
The funny part (if there is one) came when started the engine while the car was jacked up in order to change a front wheel. The wheel that was not touching the ground was spinning. I could not stop it with my hands, which means that there was enough transmission to the wheels even when the gearshift was in neutral.


Has anyone an idea what the problem is and now serious?
Thank you