I had similar problems about a year ago on my '99 R1100R.
You'll want to check:
1. Alternator. Your brushes may be kaput, and that means your entire electrical system is running on the battery, rather than the generator. Because of this, your battery, in turn, has been deep-cycled and is thus unhappy. This is the likely cause. It's not something bikers think about because 95% of bikes don't have an alternator, but rather a crank-driven thingy. BMW bikes have honest-to-god car-style alternators, and a bike of your vintage is approaching the age where the brushes will need replacement.
2. Hall-effect Sensor (aka crankshaft position sensor). Less likely, but check it out anyhow. If your alternator is going, the insulation on the wires leading to your HES are also likely dead.
Both parts may be had from a place called Euro Moto Electrics. They have good prices and great service.