Working on an early K100 just now which has an interesting problem.

The engine will only run (and rough as it is) while the starter button is pressed. As soon as it is released the power dies and then it cuts out after a couple of seconds.

Any ideas what could be causing this?

Check out the connection of the Fuel Injection Control unit under the seat. The plug connector to it can become dislodged, also the pins may need cleaning. Is easy to get out. Be careful removing it as there is a clip to be moved to free the plug. As you look from the left side after removing the side cover you will see the plug and the silver unit. There  may/should be a 'pin' behind the right hand side cover to hold it in place....odds are that's not there. The whole under seat tray will lift up for you with a little wriggle.

Already checked that Okay with no joy. Used a well known working one and there was no difference.

Should have said also that fuse number six is only powered up whilst the start button is pressed too. On my bike (being only one year younger than this problem one) that fuse has no power before the engine is started, but then stays live while it is running. Is this extra info any help?

I am not so good with electrics, but the thing is you have got power to fuel pump etc if all is turning over. With what I have picked up on the forum pressing the start button powers up the fuel pump etc only for as long as is needed for the engine to be turning over and start. Once its running then the Hall Effect Sensor provides the signal and that comes into the FICU under the seat. I have a friend over here who used to work in BMW and we have each time identified this as the problem.

If you are happy with the unit AND the quality of the loom wiring into the plug [as in no breaks in it] then not too sure where to go. The whole system works via earths and if they are not good strange things happen. There are also quite a few posts about starter motor brushes doing weird things like this too and its not much trouble to get at them.

When you press the start button an earth (ground) is extended to the fuel injection relay to make it operate. Once the engine starts the Ignition Control Unit ICU recieves a signal from the hall sensors and it then sends the earth to the fuel injection relay to keep the engine running after the start button is released. If the engine does not start the earth is kept on for 1.5 seconds after the start button is released.
The hall sensors are working because the engine fires and will keep running if the start button is held down.
The problem is most likely in the ICU or plug so, if you can, change the ICU for a known good unit and clean the pins on the plug. The ICU is under the front of the tank up against the steering head.

A check of the wiring schematics shows that All Roads Lead To Rome...... or in this case, the ICU. I think Rick will be spot on.:cyclops:
The ICU plug has a habit of coming loose because it's only held in place with the rubber cover. There have been a few problems relating to this. The contacts probably need a good clean with DeoxiT.