2002 BMW X5 loud whining noise when placed in drive . ?

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Put in another Low gear and see if you move forward.  If you still get the whine then there is an issue in the transfer case.  It might be a simple shifter adjustment to make it the correct length, as it is only touching gears together, so not engaging.  Mechanic can do that. Fairly quick as you pay for time he has to work on the car.   I am thinking shifter linkage is out a smidge...due to wear over the years.

Don't have a Beemer but another German vonder machine and the plastic shifter cups were worn out on the 5 speed.  Changed all the cups for new and it shifted like new (so we are talking out by 1/16")  I am guessing going by my car which is older than yours.  Transmission is fine.  So in this case, transfer case is fine. I don't make money doing this.  "I am GUESSING without owning  one of these cars" So you win if I am right. Parts cost maybe $25  Time to put in 30 minutes so you get charged for an hour(minimum charge) so $200(because you won't take out his ugly sister or for some other reason)and they know they CAN get the money from you.

It was the transfer case and front drive shaft .. 

HOW MANY MILES< here? you have a ZF transmission from GERMANY< that supplies nearly CAR makers globally with TRANSMISSIONS! I would tow the car to a BMW dealership and get your FLUID CHANGED and hope from there! It maybe LOW fluid only, but these ZF trannies are made so that the FLUID takes on ALL THE WEAR< and protects the pricey TRANS bits from failures! You have NO dipstick here! It is a SEALED SYSTEM and perhaps you have a LEAK somehow from a BAD road hit! The REVERSING gear takes LESS fluid to work! IT is POSSIBLE that your DRUM SEALs are BAD! Seen it on my brothers BMW X5. The DRUM SEALS are made to last the lifetime of the car, but ONLY if the fluid is changed on schedule! TRANS FLUID has coefficient of friction that WEARS OUT with mileage! IT also collects moisture, and just plainly AGES! The FRICTION coefficients wear out! USE ONLY PENTOSIN or ZF fluid! (same thing)  MOST ZF trannies have DRAIN PLUGS on the torque converters! MY TWO BENZ cars had them! SO EASY to get ALL the old bad fluids OUT and the NEW FRESH fluid in! TODAY nearly ALL domestic cars use ZF trannies and even STEERING SYSTEMS! It is a SEALED SYSTEM so there is NO dipstick! If you HIT something in the road and the pan got, hit, you could be dropping FLUID everywhere! ONLY THE DEALERSHIP has the Right equipment to change the FLUID! And I would NOT t rust an OIL CHANGE Center with this car! They use UNIVERSAL fluids, and there is NO SUCH THING as UNIVERSAL FLUID! Not even UNIVERSAL OIL! Oil is made SPECIFICALLY for each car type and each part of the country the car was MADE IN! ANYWAYS< end of mini lecture> ???ALL The ZF made trannies REQUIRE a full DRAIN and FILL, and many have TORQUE CONVERTER DRAIN PLUGS! ZF supplies KIA, HYUNDAI, FORD< GM< CADDY, LINCOLN, BMW, AUDI, some BENZ cars,  most FORDS and CHRYSLER cars made AFTER BENZ took over! The QUALITY of the ZF trans and DIFF are UNQUESTIONED! They RULE racing and the DUAL CLUTCH is made by ZF as well! This tranny has NO TORQUE CONVERTER nad shifts DIRECTLY from COMPUTER COMMANDS! it is FERRARI RACING TECHNOLOGY put t othe GENERAL PUBLIC!  I wodu BET that the FLID is low from a LEAK! YOus houdl take it to BMW and let them CHANGE the TRAN FLUID and NO WHERE ELSE! Is uses PENTOSIN or ZF trans fluid ONLY.  THey can DUMP a DRUM SEAL easilyif the FLUDI is TOO OLD!

if driveshaft or t-case you would have no reverse either. you have a internal transmission problem. find local shop at ATRA.COM 

A bad transfer case and driveshaft will only make noise while the car is moving. You're going to need a transmission.