I am using ubuntu 10.04 on dell N5010 with perfect battery but it get immediately hibernate after removing power cord. battery is charing during ubuntu use.
Did you check out battery status in setup by hitting F2 in boot menu? Did you see your battery's health in Windows. I am running Dell 1545 and Dell 1525 both with Ubuntu as primary. I also ran into battery related problems recently. Replacing it solved the problem.
It is almost certainly a hardware issue. Get a new battery.