I'm not an expert, usually dont ever need a new battery, replaced the one on my sprint after it left me stranded, but I had left stuff turned on by accident and totally drained it a few times... and it was from 2001!
BUT I think I read somewhere that as a battery gets older, that it may show charged but not have enough cold cranking AMPS or whatever the technical term is to actually turn over the bike.
it takes a good amount of juice to turn a starter.
BUT, Id swap another battery in from another workign bike to see if its the bike to be sure, before I ditched it.
you can also take the battery and have it load tested. not sure if an auto store can do it, maybe?