This is a very frustrating problem that must be driving you nuts. Sometimes, when I had similar problems, I would drive the car up on ramps, or jack up the front of the car so I could get to the starter terminals. I then would get jumper cables and hotwire the starter. As I told the rest of the boys, I haven't used my z3 since I drove it home from buying it so I'm not that familiar with everything on the car. So my experience is with other cars. I say this because I don't know where your starter relay is. Its usually on the starter but could be on the firewall. As you know, the largest wire coming off the battery is for the starter. nothing on the car uses as much electric so quickly as the starter. But it starts out as a wire that has connections added to it so it can be hooked up to the battery and the starter. If the problem is in this wire, it will be at 3 possible locations. Either where the wire attaches to the battery connector, where it attaches to the starter connector or a break in the wire itself. Breaks within a wire are the most difficult to detect because they can make a temporary connection and fool you. This is assuming that your connections to the starter and battery are clean. One of the boys earlier, I think it was Aceman, said to get to basics to track this thing down and he's perfectly right. So, when the car doesn't start, and you're able to get under the car, attach the positive jumper cable lead to the terminal the battery lead is attached to and the negative lead to the body of the starter. The other ends of the cables should be attached to your battery. Please note:THIS CAN BE VERY DANGEROUS. You have to be very careful that your cable leads aren't touching anything they shouldn't be touching. YOU MUST BE SURE YOUR IGNITION IS TURNED OFF WHILE DOING THIS. YOU DON'T WANT TO RUN YOURSELF OVER. Doing this will hotwire your starter directly from the batter. The only other electrical wire that needed is to the starter solenoid. Since you hear a "click" when you are trying to start the car, this wire is working. If you are at the point where you have hotwired the starter, get in the car and turn the key as you normally would. If it starts, then there is some problem with either the ground wire from the battery to the car, or the hot wire from the battery to the starter. If you try to start it and it doesn't click, then your starter solenoid wire should be hotwired. This is the dangerous part since you are bypassing all your safety switches and precautions. If your car is in gear while you hotwire the solenoid, your car will move so YOU MUST BE SURE YOU ARE IN NEUTRAL OR PARK AND YOUR HAND BREAK IS ON. Block your wheels. Doing this eliminates EVERYTHING but your starter and battery.