if the engine is turning, that means the starter is working and the battery is ok.
I'd say the starter is the device that would absorb the most power out of the battery. So if the engine is turning it means the power is there.
the "buzz" would bethe fuel pump. that is missing. without fuel pump an EFI engine won't run. I'd say...obviously is the switch on the RUN position rather than OFF? maybe a bad contat there? the fuse of the fuel pump?

 

Here's another vote for a bad battery. It only cranks for 30 seconds then can't go any more, but the charger thinks it's charged after 30 minutes? There's a dead cell in there. Make sure the new battery is fully charged before you install it.

If it only sat for a few months there shouldn't be a problem with the gas.

 

If you use this method to check for spark, screw another spark plug into the head. Late model Harleys won't send a charge to the plug if there is no compression because of the ion sensor.

It sounds like you need a new battery.

 

I agree that if it can turn the starter, there is enough juice for the fuel pump. The fuel pump fires before the starter, so if no fuel pump, I'd be checking the pump end of things first. Get the pump running then see about the battery. You don't need the starter draining the battery to check the pump. You just need to turn it on.

 

i say fuel pump also