BMW X3 not turning on? no crank?

Most likely is the battery. Test out the battery first before you take it to a shop if you can get one of those battery testing scanners. Could just be a dead battery.

REMOVE the BATTERY and take it in for testing and CHARGING! REMEBER THIS though! You MUST use a genuine EUROPEAN BATTERY and NOT a throw away LOW MAINTENACE one! There is NO COMPARISON between a REALL BATTERY and a CHEAP BATTERY from AUTO ZONE! Get a DEKA or a n INTERSTATE or 9one from the BMW< AUDI< or BENZ dealership ! or even a TOYOTA battery! USUALLY you must replace the BATTERY and the ALTERNATOR at the same time! BUT< perhaps this car SAT on a LOT for a LONG LONG TIME and the RADIO Memory and CLOCK used up the power! SO TRY to get a GOOD RECHARGE here! CHEAPER BATTERIES will cause electrical problems with these cars !THEY RELY on SUPERB electrics  and a Battery made to the HIGHEST precision to be "HAPPY"! Worked on a few AUDI CARS that REJECTERD the new AUTOZONE battery! Nada one BENZ that went through THREE of them until it got a REAL BATTERY with a HUGE warranty! AUTOZONE Only gives a TWO YEAR WARRANTY! I have work3d on BENZ cars that had ORIGINAL BATTERIES in them after 15 years! THEY STILL WORKED FINE! It's WHY AMERICA cannot be GREAT AGAIN! Our STANDARDS are SO VERY LOW! Its all about QUICK FIXES and NOT QUALITY! OUR CARS keep getting better as more and more SUPPLIERS are from GERMAN or EUROPEAN companies! A FORD edge is HALF FORD and HALF AUDI! the BEST parts are AUDI! ZF< the company that supplies TRANNIES for BMW< AUDI, PORSCHE< and some BENZ cars, is NOW supplying almost ALL CARS with great MULTIPLE GEARED trannies with SHIFT PADDLES! The MANUMATIC ones are AWESOME! NO TORQUE CONVERTER! Thanks to ZF engineers! I INVENTED this I thought, but they beat me to the PATENT OFFICE! ZF makes STEERING SYSTEMS as well and MAYBE even ELECTRIC AC parts! OUR CARS were NEVER made to get to ONE MILLIONS MILES< whereas EUROPEAN cars ARE MADE that way.  I can't believe that there are STILL PEOPLE out there that go GA GA for GM CARS when hey Are some of the WORST made cars in HISTORY! DOORS that SAG! BRAKES so over boosted you end up going through the WINDSHIELD and even NOW they have BILLION DOLLAR LAWSUTIS for ignition switches that CATCH ON FIRESM and AIR BAGS that deploy for NTOHING and kill KIDS and PETS by accident! Even MAIM them! NO WONDER TOYOTA and FORD lead the way and ALSO VW< the HIGHEST seller worldwide! It SEEMS like ALL auto innovations come from GERMANY m, BOSCH and DENSO of JAPAN! WITHOUT Germany ZF< we would have NO CARS JUST GAS GUZZLING monsters with ONE WHEEL DRIVE!

Budget at least $750/month for repairs on that car.

Amended:  OK, make that "save" $750 a month for repairs . . . Yes, there will be months when it isn't in the shop - but others when it will cost thousands to get it back.

You’re going to need a charged battery to check for problems anyway.

So remove and fully charge the battery. But the fact that even the security light isn’t blinking strongly suggests either a totally dead battery which won’t hold a charge, or simply a loose battery connection. That could be at the battery itself (most likely) or where the red (positive) battery cable meets the starter motor (only likely if the starter has been changed just before you bought the car) or if the black (Earth/ground/neutral)  battery cable has a poor connection where it bolts onto the car body (usually due to corrosion, and X3s do tend to get rusty).

A 2006 car should be at the stage where it needs it’s battery replaced for the second or third time. The original will typically last 6-7 years, a top quality replacement around the same, or a budget replacement tends to last about 3 years. 

Most obvious reason is dead battery or dirty/loose battery terminal connections

Battery is flat. Disconnect and charge it. Even if it starts you should think about a new battery before you get stuck a long way from home. Test it. See link.