I've had a similar issue on a number of '01 740i's. I'll have to check out the paper work. Sometimes a fresh battery cures it, but often it's something in the starter or starter relay. Clicks just like the battery is nearly dead, but it's not the battery.
I'm sure that was absolutely no help to you at all...
It does seem to be a common problem, at least on the 740's.
Occasionally, repeated attempts with a known fresh battery will get you going. Just keep clicking away and eventually, it just starts up. I know that's not fixing anything, but it may prevent you from being stranded.



Gar