I've traced the cable from the security alarm control into the relay box. 


It's clear which connections relate to the security alarm harness.  I plan to simply disconnect those.  I have located the black/yellow wire from the right handlebar switch, which I understand to be the key to energizing the starter.  After I disconnect that from the security alarm loom, where should I connect it?  Secondly, there's a white plastic connector in the right side of the relay box. It connects two wires from the OEM loom to two wires from the security alarm. (Actually, the OEM loom has four wires entering, but two end in the plastic connector).   What should I do with the four after I disconnect the alarm wires? Tape over the plastic connector?  Connect them somewhere else?
Thanks for your patience.

To bring closure to my work to remove the security alarm and wiring harness, I'll add this.
I removed alarm control and the wiring where its harness connects to the BMW OEM wiring.  As suggested, I reconnected the red/black wire to the starter relay. The engine thereafter sprang to life at the touch of the magic button!  The brake lights work, the indicators work, everything seems to be operational.  
That alarm system is quite a puzzle.  If BMW originally planned for the white barrel connector (in the relay box) to be the point of attachment, how could that straightforward approach have been so completely subverted by that complicated harness I found on my LT?  Weird!
The security alarm wiring harness' ground (brown) wire attached to the multi-wire ground on the frame behind the steering head.  That wire was virtually toast when I removed it.  However, I couldn't find any evidence of corrosion at the ground point.  I have yet to discover what caused that fried wire and blown fuse.  
At this point, I have removed the alarm wiring, but there is still that mystery wiring of six strands that is connected to nothing near it's end at the computer for engine management. Since all seems to be well without it being connected to anything on both ends, I assume it had nothing to do with the alarm system.  Those bundled wires run along the left side of the frame and vanish into the area behind the plastic cover over the handle bars. The bundle must be at least 7 feet in length.  When I have a good reason to dig into the steering head area, I'll no doubt discover what they connect to.  Meanwhile, I'm entertaining guesses as to what they may be (or were?) for.

I've now been around the block a few time with failed attempts to find the code that would allow the radio to be turned on.  I've spoken with a BMW dealer, with BMW north America customer service and have listened to a couple of K-bike owners advice on another forum.  I've concluded that the radio I have will never operate.  New decision to make: try to fit another (non-BMW) unit into the space provided in the fairing or turn the space into another glove box.  I'm leaning toward the latter because I can always carry a small portable radio to monitor weather forecasts when touring. However, I'd like to learn what others may have done, both positive and negative experiences regarding the K1100LT radio.

I bought a AM/FM/SW/MP3 player from Jaycar. It can store 1500 to 2000 songs, it currently has about 300. I can also listen to my GPS instructions. The only downsides are that on the fitted internal battery the MP3 and GPS instructions only last about 2 hours. I have got around that two ways I have a power pack backup about the size of a phone, or I can plug into the bricks auxiliary socket. The other slight downside is that I have to put a piece of tape over the channel knob to keep it on the correct FM channel for the GPS. It cost me about $30.00 AU on special.

Regards Martin.