Gas tank bmw k1100rs - 1996 BMW K 1100 RS

check the fuses, if good the pump burned out.

Your bike uses a fuel pump which was the origin of the noise you used to hear. Now your pump has died and must be replaced.
This is how the pump is mounted, how you remove the tank coder to access it and where to order a new one
http://www.bikebandit.com/1993-bmw-motorcycle-k1100rs-5-speed-transmission-drive-shaft/o/m60sch350445 

I would be thinking more about a decent second hand K1200RS - far superior in every way to the K1100RS. Plenty of good used examples around at reasonable prices and a huge aftermarket options list. You should be looking around US$5K for a 2000 model MK1 RS and it will do everything you can throw at it.

You should use BMW Oil 20-50

You should use BMW Oil 20-50

You should use BMW Oil 20-50