Sorry to harp on this, but I'm gonna.

I had never had this happen to me, ever. Then, on Sunday it happened with my
motorhome, and I was trying to sell it. The buyer asked if he could start
it, I tossed him the keys, and it cranked and cranked but refused to start.
It had never done that before, I often will start it by simply reaching in
the window and give the key a quick twist. It never cranks even a full
rotation before it starts, but Sunday when a buyer was looking at it, it
cranked and cranked, and cranked some more. I looked at some stuff and tried
to get a fuse out, but couldn't. I tried again and it started right up. I
was thinking I would need the tow truck to get it home, but it turns out
that I was having exactly the same trouble as you guys had. I had a previous
looker about an hour earlier and he wanted to turn the generator on, but the
gas tank was approaching E and there wasn't enough gas for the generator. I
took the vehicle over to the gas pump, 50 yards away, and put in $50 so it
wouldn't be E if somebody wanted to go on a test drive or take it to a
mechanic. After getting the 50 bucks of gas, I drove it 50 yards back to the
spot where it was. Of course, I started and stopped the motor at the
beginning and end of each leg of the 50 yard trip. About an hour later, a
second looker wanted to hear the engine run, and this is when it refused to
start.

What happens on short runs like that is the plugs get very wet, dripping
wet, with fuel, and the plugs don't spark well when they are that wet. There
are two ways to dry them, pass lots of air over them, or wait for the gas to
evaporate. One method takes several attempts at starting and might seem like
endless cranking, the other method takes a very long wait.

Granted, my motorhome and your BMW share very little other than they have
engines and tires. But the engines in both are fuel injected, albeit the BMW
is a vastly superior system, and the fact is that I used my motorhome in
pretty much the same manner as you used your car before it decided to not be
your friend anymore - we both drove very short distances that involved two
or more starts very close together with extremely short run-times. I would
not have thought that the short trips were the cause of my troubles, and
when you related your story it took me three days to think about what you
went through and how it is nearly identical to what I experienced.

The good news is, there is nothing wrong with your car and you don't need to
worry about it. The bad news is, you paid somebody to turn the key a bit
longer than you attempted to turn it, and you lost a day waiting to get your
car back.