My '95 850 has had a similar condition 5 or 6 times since I bought it new. After having it towed to the dealer the first time, they started it in the parking lot by engaging the starter and continuing to turn the engine over until it finally started. (Just like you would do for an old car that was flooded). I now do the same thing whenever this happens and it always starts eventually - just keep turning the engine without pressing on the accelerator. It could take 30 - 60 seconds (or maybe longer) of cranking to get it to start. There does not seem to be any particular time or weather conditions when this occurs. Once it starts, I can turn it off and it will start up normally again. I assume it is something in a relay or some other electronic part but I've never been able to determine the exact cause.
If this does not work, below is a link to some responses to a similar question on the board. Some other things to consider and try. You could also do a search for "won't start" to get a lot of other responses. Good Luck.

http://www.brickboard.com/AWD/index.htm?id=437024&show_all=1