MacBook Unibody 2009 Battery Issue

I have a MacBook Unibody 2009 and am facing a weird issue. My laptop only works when it's connected to a power source but not on battery. As most of us would, I thought the battery was gone so I bought a new battery. However, after charging it I still had the same issue. So, I took it to a repair person whom I know and he told me it's some issue on the motherboard. Now I am not very sure how accurate his diagnosis is. Does anybody here know of or have a similar issue concerning MacBooks? Can anyone share some information on this?