To me it sounds more like a loose connection somewhere as normally the batteries just start to hold less charge over there lifetime and you therefore get less runtime.
I guess the loose connection could have either been on the battery or it may be on the power connection on the laptop itself.
As for the moral question a bit of a grey area really yes the battery isnt normally covered for the reason I stated above but if it is down to a loose connection somewhere along the line then to me that would be a hardware fault and I would argue my case for them to repair it under warrenty.
You state that you have already purchase a new battery so I would see what happens when this arrives. If indeed it is a loose connection which to me it sounds like you may find you still have the same issue in which case repair under warrenty and if your feeling cheeky your money back for the new battery.
To me if it was the battery just begining to hold less charge it would not just cut out you would get a battery warning in windows and/or the battery light on your laptop flashing