That sounds like a sticking sprag. In- between the starter motor and the engine is a sprag or one- way clutch which engages when the starter is turning faster than the engine. It sounds like yours is sticking a bit although I am not quite sure how moving the rear wheel 'fixes' that as that won't turn the engine or primary drive unless the bike is in gear, which you already said it is not. File that under things that make you go 'hmmmmm'.
I did take a quick look and removing the starter is not particularly difficult. The starter clutch (and sprag) is another matter: the manual says that the first thing to remove before removing the starter clutch is the.... engine! Yikes. As I remember, you are riding a 2010 which would still be under warranty so that might be really good news.
The first thing I would try would be to change the crankcase oil; the sprag is lubed using that oil and if it is dirty or on the thick side (say a 15W or 20W weight) using clean oil, perhaps of no more than a 10W weight could be the fix. You might want to consider even a lighter winter weight oil- say a 5W weight (like 5W-40 but no lower on the second number).
Best of luck with this Wayne and I think this is the first time I have heard of this on a C-14. By the way, mine performs flawlessly down to 11 F and has for years and going by the reports of others who ride these bikes in the winter (northern US), it certainly does not seem to be a chronic problem on any kind.
Brian
Ok, so here it is...
When I first try and start the bike on a sub 40º morning, the starter spins, but, does not engage. If I put it in neutral and roll it forward or back a few inches, or rotate the rear wheel while up on the centerstand, it will start as normal. Fully charged Batt.
It will start normally the rest of the day. What say ye?
