You posted at f650.com & WPoll provided answers & links
The majority of the dash lamps are directly driven from neutral/high beam/BMSC so are independent of the dash electronics
The dash electronics are clearly attempting to initialise and failing then attempting to start over and over again, you will find threads about it at f650.com
With all the 650GS models particularly the dual spark & G Series it is not a good idea to turn on ignition when the battery is bad
Without the bad battery aspect in your case the most likely problem is the 5v supply rail electrolytic capacitor degrading due age & the way stepper motors work
If you don have good electronic skills find a good electronics tech & have him clean the pcb & replace the capacitor