About to give up.

Mick look at the small items first. I would lift the tank and remove the bear claw and follow the wires very slowly. It sounds more like you have a bare wire getting grounded out. I would start at the battery first since you just replaced it. Why I think this is because the only thing you are doing is turning on the key and it is blowing the fuse. Be sure to check that your ground wire is grounded good it could have came loose.

STARTER RELAY AND HARNESS CHECKING IF YOU DO NOT HAVE THE EXPERIENCE WITH A VOLT YOU SHOULD NOT ANY OF THESE THINGS!
STARTER RELAY ITS SELF
OHM METER FROM #4 TO#6 ABOUT 85 TO 88 OHMS
YOU CAN PUT POWER IN ON #6 AND GROUND #4 YOU SHOULD FELL A CLICK AND WHILE ENERGIZED YOU SHOULD HAVE ABOUT ZERO OHMS ACROSS #1 AND #8
YOU STILL COULD HAVE BAD CONTACTS OR BAD TERMINALS

CHECKING STARTER RELAY HARNESS WITH RELAY UNPLUGGED
KEY ON OHM FROM BAT GROUND TO #8/87 MINE CHECKS .4 TO .5OHMS CHECK VOLTS FROM #6 TO BAT GROUND SHOULD BE 12 VOLTS WHEN STARTER BUTTON IS PUSHED.
CHECK OHMS FROM #4 TO BAT GROUND KEY ON IN NEUTRAL/CLUTCH LEVER IN METER SET AT 200 MINE IS 27.4 OHMS.
YOU CAN TAKE 5 WIRES PUT A MALE AND A FEMALE TERMINAL ON EACH WIRE (PREFERABLY DIFFERENT COLORS) HOOK UP THE WIRES EXACTLY LIKE THE RELAY PLUGS IN BEING REAL CAREFUL WITH #$ AND #6.
THAT WILL MAKE IT EASY TO TELL WHAT IS GOING ON.
IF THE RELAY IS NOT CLICKING YOU PROBABLY DO NOT HAVE 12 VOLTS COMING FROM THE STARTER BUTTON #6 OR YOU DO NOT HAVE COMPUTER GROUND ON #4.
MAKE SURE BIKE IS IN NEUTRAL YOU CAN JUMPER FROM BAT POS TO #6 AT CONNECTOR TO BYPASS STARTER BUTTON.
MAKE SURE BIKE IS IN NEUTRAL YOU CAN JUMPER FROM
BAT NEG TO CONNECTOR #4 THIS WILL ELIMANATE THE COMPUTER GROUND.
MAKE SURE BIKE IS IN NEUTRAL YOU CAN JUMPER FROM BAT POS TO #8/87 AT CONNECTOR TO BYPASS ENTIRE RELAY ASY. MOTOR SHOULD TURN OVER.
THIS IS JUST A GUIDE AND IS NOT MEANT TO COVER ALL PROBLEMS.