MY Z3 DRAWS BATTERY POWER WHEN PARKED AND RUNS DOWN BATTERY WITHIN A DAY OR TWO. SOMETIMES HAZARD LIGHTS ARE FOUND FLASHING WITHOUT ALARMM SOUNDING.

SOURCE: mysterios drain on battery 1996 BMW Z3 1.9

look at the dome light switch on the drivers side for corrosion etc. make sure it isnt pulling the circuit down

SOURCE: Does the 1994 320i come with an anti theft system.

you may find tha the locks need a good oil, and the pasenger sid as it dont get used , they may of both gon stiff and the micr switch tha sits next to the lock barrow is thinking its still locked .. my bmw used to lock me in wen a slamed the door

SOURCE: 97 bmw z3

You may have a starter or ignition switch issue. I would guess starter with just the information you are giving. Of course with electrical problems proper testing needs to be done to condemn expensive parts such as a starter.

SOURCE: 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!

SOURCE: killed battery by leaving lights on. Went back

your alarm system causing problem