Install a new battery. We had that just yesterday when I wanted to help soneone with an E31 850. His battries (he has 2 in parallel) were close to complete empty. Tried to start the engine, a few clicks, then nothing. Lights in cluster dark, no doorlock functiong, no window etc.
Then we tried to jumpstart with my 750 with my engine running, nothing happened. I tested with my DMM, on my plus ploe and ground it was 13.2V, on the jumper cables around 6V only, no matter if we tried via engine room or the batteries in the trunk.
Both batteries were completely dead. The jumper cables/wires were hot from flowing ampere, but half of the voltage. You can calculate that.
what I mention about the batteries and voltage drop is not uncommon, especially if u have a bad battery in the car u are trying to start. In our 750's sometimes the cable does not get a good grip on the battery pole under the hood.
you can measure between the jumper cable connector and what ever it is you are connecting to. you have 4 connections, 2 in the 750 + and -, 2 in the 850 + AND -, if the car to be started is really dead, then u have a lot of current flowing through the jumper cable maybe as high as 30 to 50 amps. after all, there is no current control, the alternator just sees a big load.
if you have 4 connections and loose 6 volts, that could be only 1.5 volts per connection. if you were only drawing 10 amps, then the resistance per connection only has to be 0.15 ohms {V=IxR, 1.5=10x0.15), if the current is 20 amps u only need 4 connections with a resistance of 0.075 ohms each to loose 6 volts ! so you see, it is quite plausible to loose 6 volts over 4 connections, best way to find out is to measure across each connection and see which one drops the voltage.
As for the fuse, there is a fusible link close to the battery on every BMW, wherever the battery is located, engine room, trunk room or under seat, always very close to the battery.
http://www.bmwe34.net/Wiki/tiki-index.php?page=Fusible+link
@EuroShark: the 750 has 2 fusible links, at least the E32 750. Very tricky, one is behind the battery in that black plastic, the other one is hidden inside plastic wrap on the red wire from battery plus towards the funnel under rear door where the loom goes towards front and from there into the engine room thru the firewall.