Zoros, you don't need to take the gearbox out, but you do need to remove the centre console and the gear selection module itself. If your car is stuck in park, you will not be able to remove the centre console without first hammering the gear lever out of park - when my (out of warranty) R230 had this issue in 2009 I managed to do it all myself by following one of the youtube guides that are out there. It takes confidence and patience, but can be done by a non-mechanic.
I bought my replacement part from Monoglobal in Australia, via Ebay I think. You can have a plastic part or a more sensible metal part as a replacement.
I doubt you will obtain a part number as the 10 pence plastic piece that causes the problem is part of the bigger mechanism, and this is the part which will have a part number...as well as nice big price tag. The whole mechanism if bought new from MB will need to be "tied" electronically to the car, which is why buying a second hand one tends not to be the way to go.
Sometimes the car being stuck in park is not actually caused by this part failing, but by a dodgy brake pedal switch. Hope you get sorted!