Are you getting those voltage readings from a meter (DVOM) hooked directly to the battery, or is that on a gauge on the dash? If it is dropping that far reading directly off the battery, I would say the battery is toast. If you are getting your readings from a gauge on the dash it sounds like there is a bad main power connection, but still could be the battery.
"Big Bad Wolf" 2004 Sportsman 700 EFI, Mine
"Lil' Red" 1999 Sportsman 335, The Wife's Ride