I live in Ga too so its cold out side.
Whats wrong with my bike? - YouTube

 

Battery sounds low. Low voltage wont fire the electronics up. Put a voltmeter on the battery while your cranking it and see how low it goes.

 

Would it be better just to buy a new one?

 

Keep the bike garaged or outside?

 

New is always better. A new battery never hurt anyone...

I like to test things first to avoid buying stuff that is not needed, but to each their own.

 

Autozone checks and charges battery's for free... There not a bike shop and 90% of the time don't carry that type of battery so you know if they tell you its bad there not just trying to get money outa you... not sure if there on the east coast though