Had a similar problem with a non-BMW car...Tried to kick over but engine does not burst into life. This went on for a couple of days and I had to recharge the battery after so many goes at it.
Basically, I think it was down to dampness. The weather went very cold and it coincided with washing the car as well (so probably condensation as well). Think that type of car cannot cope with dampness. Mind you, I have not heard of similar issues with BMWs.
Check if your engine bay area is damp...to get a clue if your problem is like above. Then check spark plugs are not wet/damp (I dried them with a blow dryer) and wires in the engine bay are good and dry (and good connections). After making sure all wires I could see are dry, I sprayed them with a dampstart spray (which is suppose to help reduce dampness).
ps: Make sure your battery is good...or at least have some means of re-charging it if it runs flat.