Need Diagnostic Analysis

I have a fifteen inch uni body macbook pro 5,1
I am experiencing odd behavior with the battery.
Often, when the charger is connected, the charger icon indicates that there is no battery connected. If I disconnect the battery charger, the computer will die.
Then, at times I will see the battery charger amber light and the system indicating a percentage. It will run on battery for a while but then dies before the percentage drops down to whwere you would expect it too. In other words, not long.
I brought the laptop into a genius bar and they told me I needed a battery which I bought. However, the problem persists.
I did the PRAM and power management rests to no avail. Any clues?
Thanks