Resolved Laptop new battery won't charge

I am working on a Toshiba Satellite P35-S611. I was called to work on this laptop because originally the thought was the power jack had come loose from the motherboard. I took apart the laptop and the power jack is securely connected to the motherboard. I can jiggle the power cord to a certain point that the laptop gets power and the battery light comes on. I think the power cord needs replaced, thinking the prongs inside the connecter are not getting proper contact. Or maybe the power jack on the motherboard has gone bad but I have never run into that problem before. But I don't understand why the battery does not charge if the battery light is coming on. The client said they bought a new battery.

 

As far as I now the battery is a match. I was afraid it might be something like motherboard or jack. Are those still possibilities even if the laptop gets power and powers up fine. Even if the battery light comes on that may not mean the battery is being charged?
Thanks for the fast response!

 

Where I live there is no Toshiba testing center. And none near by. For now I will tell the client what the problem possibly could be. It would be nice to have some kind of testing kit that I could use for future problems. Does anyone know where I can find testing kits that might help on future laptop problems.