2000 BMW Z3. When it rains and my car is parked

I had this same problem - 2 things to check:
Most likely it's the 3rd brake light - check the seal on the inside (you need to remove the black plastic cover inside the boot lid to be able to see - this has 4 or 6 little tabs that hold it in place and break very easily, so take care as you remove it. I suggest using a blunt knife or similar to ease it out). I had mine replaced not that long ago and as far as I can recall they're pretty inexpensive.
Also check the rubber seal that goes all the way round the boot opening, make sure it's attached all the way round and has no defects.
Hope that helps!

I had this same problem - but now that I replaced the battery the car still won't start - I get the lights now but it won't start. Any ideas? Thanks!