Southern

Hello everyone, I'm regretful that my first post has to be in the technical forum but I really need to get this fixed, so thanks for your time. I am also new to motorcycles and have a very limited knowledge that I hope to improve, so bear with me. Anyway down to the problem, a few days ago I go to start my 09 YBR 125 (fuel injection model) as normal, when I push the ignition switch nothing happens. I try the kick starter which eventually gets it running, but I notice that the rev counter is quite sporadic, jumping about. It does settle down after idling for a minute and I decide to take it out, at this point I believed that the battery was a bit low or something because I hadn't used it for a week or two. So It seems to run ok for a minute and then I noticed the rev counter is showing 0, occasionally flicking upwards, at this point everything dies and I completely lose power. I give it another go but the same thing happens so I push it back to my house (up a massive hill). Still thinking it's the battery I take it out and leave it to charge overnight. The next day I put the battery back and nothing has changed, so I decide to check a few things. When I start up my bike in still makes the whining noise (fuel pump?), the engine light comes on and goes off as it should. If I pull either brake, press the ignition, press indicators, the neutral light dims very rapidly and slowly lights back up. All this seems electrical and for me it points to the battery again. My battery charger states that it's fully charged, so the only thing I can think of is that it's dead. I'm going to buy a new one tomorrow unless any of you believe that my problem isn't the battery. Thanks.