Bad contacts in the ignition switch. Either buy a new ignition switch, or taker out the old switch and use a nail file or emery board to clean the contacts. Plenty of Youtube videos on this. This was a problems back in the days when the ignition still used points in the distributor.

Something you can check that won't cost anything is the computer modules in the box under hood on the passenger side... I had a no start issue that was because of corroded pins in one connector. Worth a gander to make sure all is in order there...

A couple of people have had trouble with the green relay that controls the starter circuit. You could switch that relay with one in another position or just throw a new $15 relay at it. The electrical contact part of the ignition switch is separate from the key part, and is only $30 or so.

I had an intermittent start issue once that was a loose wire at the starter. But had started to back off. Was under there and noticed it by chance... But, Don't put a wrench on the starter terminals without disconnecting your battery.

Quick update: I got in the car this morning and it did the same thing as yesterday morning - no crank when I turned the key. Just to see what would happen, I shifted it into neutral and tried again. And it started right up. I'm wondering if this is indicative of the problem?

Later in the day I ran diagnostics on it and nothing came up. No fault codes were stored.

I had a Volvo 960 several years ago and it had a bad PNP switch and behaved in a similar way. I also presently have a 1992 Ford F-150 and it also has a PNP switch that's on its last legs. But in 20 years of BMW ownership, I've never had an issue with the PNP switch, but that's starting to look like what's going on.

I also would be looking more at the transmission position switch. Sadly it is $390 list and about $280 from the usual discount sources. The switch and its connector are under the car and exposed. Probably worth crawling under there and unbolt it to give the switch and connector a good clean with electrical contact cleaner and some deoxit.

Pelican posted a DIY if you want pictures.

Could also be the inhibitor switch.

http://i260.photobucket.com/albums/i...itorswitch.jpg

Here's a picture of the switch removed from the trans.

https://c1552172.ssl.cf0.rackcdn.com/285600_x800.jpg

Great pic, thanks! I'm going to experiment a little more before throwing a $300 part at it, but at least I have a strategy now…

If it starts in neutral, you can always use that procedure instead of starting in park. I replaced the neutral safety switch for my Audi A6 Avant which was a ZF 4HP18 trans. The car would always start, but it would throw up a Trans Fail message. The plastic for the switch had hairline cracks in it so sometime it wouldn't make contact.

I'm going to try it for a few days and see if it will consistently start in neutral (it may have been a fluke yesterday). If so, I'll remove and clean the safety switch and see what that gets me.

cleaning
 

I had questioned mine and removed it. It is riveted together, but you can drill those out and use nut/bolt for reassembly. Pretty simple unit, your contacts may be dirty and just need a cleaning.