Diamond key replacement batteyr DIY (NO 56K)
Must use rechargeable battery - Panasonic or equivalent.
It does charge by induction when in the ignition driving.
If cutting fob open do not let blade go deeper than 2 mm.
If the fob won't initialize the new battery may be flat so use it in the car or sit it on a 3 volt source or close to - eg phone charger.
Replacing the battery is not hard just be careful not to damage the PC board and don't overheat the battery when soldering.
www.BMWGM5.com has product and some good advice.
Miles of batteries on eBay.
$300 per key from BMW here. What have you got to loose - have a go.