BB Curve 8310 :: Turning Itself Off Randomly

I just bought a used 8310 from a bidding website, and the problem ive got is the phone is usable as long as not much is being done on it, but when you start using apps like fb, msn, bbm and others(not at once) somehow the phone shuts down itself without any warning, and it cant be turned on unless its plugged to electricity or battery is removed and replaced, only to be shut down in short time after its turned on, for it to be somehow usable for some time more it must be charged for a few. I checked the status option and its got plenty free space(24mb) ive spent countless hours researching for the same problem online, and many say its the OS, but ive downgraded it, then ugraded it, rebooted it, master rebooted it, done everything to it but technically nothing works(after OS upgrade it worked perfectly with apps for around 3 hours). Oh and i forgot to say battery compsuption seems quite high, after its done charging its at 100%, then use msn and fb for around and hour and goes down to 80% couple of shut downs and turn ons after its at 5%. So, anyone has an idea what the problem might be? I dont want to buy a new battery to later find out its the phone that its deffective, and if its deffective anyone had any luck repairing it? the phone works perfectly while plugged in to an outlet or pc, it does not shut itself off at all.