Had the exact same problem on my 2002. Called a locksmith and he used the plastic wedge to insert an inflatable bladder at the top corner of the driver's door window frame. Pumped in enough air to get about a 1/2 inch gap, then used a rod to pull the inside door handle twice.

Sure, the alarm sounded, but it stopped as soon as I started the engine with the key. $75 plus a $50 trip charge - covered by State Farm Insurance.

2002 X5 3.0 313,700 miles
2014 428i 23,700 miles

2004 325i sold at 123,600 miles
2001 325i sold at 66,000 miles

1970 Firebird - Under restoration