The brown wire between the voltage regulator and the alternator is a ground wire. I had the exact same thing happen to that brown wire on my 68 280SE. Turned out the problem was the main ground cable between the firewall and engine bell housing had corroded. When i would try and start the car, the current would flow through this small wire between the alternator and voltage regulator to ground. The high current from operating the starter melted the insulation on this small ground wire. I had to cut out the burned wire an install new wire. I would definitely check the main ground cable between the firewall and bell housing. It is located on the drivers side firewall. It looks like a large braided cable with ring connectors on both ends. Remove it and make sure all of the connections are clean and tight.

When you turn the ignition key on you should here the fuel pump at the back operate for a second in order to pressurize the fuel system. If you don't hear the fuel pump come on, then i would check on the condition of wire that provides power to the fuel injection system. This wire runs from the positive battery terminal down to a relay in front of the ECU. Make sure the connection at the battery terminal is clean and tight.

Also I would also check the the ground connection for the fuel injection system. The connection is located behind the battery near the firewall. You will see 8 brown wires screwed down there. Make sure the connection is clean and tight.

Hope this helps
John