After recently buying a bike (that had sat for a while ... or maybe longer than a while

) I charged the battery up. This started the Buffalo on the electric start and also the bike kicked over easily to start. Left her for a week or so and when I turned the key, there was no neutral light or power. By pressing the horn, there was a faint, vestigial noise but nothing anywhere else. So, I took the battery out and put it on the charger. The charger immediately lit up to say the battery was fully charged

This doesn't correspond with the power situation on the bike.
Is my battery buggered and if so, why is the charger telling me it's fully charged? Or, have I developed an electrical fault?
If I need a new battery, what's the recommended one for a 72 Buffalo - as per manual or is there something newer and better?
Thanks, Mike