We need to stay on this!!
YES (just to clarify, you are talking about tranny engagment, NOT tire traction/slipping - correct?)
We need to discuss this. I have the EXACT SAME issue with my 2004 330cic. 3K miles on it. It started doing it at about 1500 miles or so. Here is my exact description:
1. Car sits in level garage overnite.
2. Start car, idle for 5 - 10 seconds.
3. Put it in reverse.
4. Back out of the driveway, fairly steep slope for about 35 feet.
5. Put it in 1st.
6. Step on gas.
7. Engine revs to between 1800 - 2200 RPM for 2 to 4 seconds - no power to wheels.
8. Transmission then 'grabs', and car starts moving.
9. It does it only once in the morning when totally cold. It does NOT repeat after sitting for 3 to 4 hours. It only occurs after 8 plus hours of sitting unused.
It seems to do it mostly after initially backing up, although I know of at least one occasion that it did it without backing up.
I have had the car into the Dealer. Explained the problem just as above. They had the car for 3 days. They said it didn't do it. But when I questioned them on backing up first, trying slope, etc. the answer was that they did not try that. I decided to pickup the car and wait a week or two. It is still doing it, so it will go back.
They told me that if they do find a problem, they will probably replace the transmission with a new one and send mine to engineering for analysis.
Mine was build in late March/Early April. When was yours built? That may be a clue....