Latitude C640 - Power Supply Issues/Failure

I have a C640 machine that is having power supply issues but I think it's more the power connection on the computer than the actual power supply itself that you plug into the machine. 

 

What's happening is when you plug the power supply only into the outlet, the green light comes on, it seems fine.  The minute it's plugged into the machine, the light goes out and the computer doesnt recognize that there's a power supply.  I have gotten another power supply from another C600 series computer and it does the same exact thing. 

 

I am wondering if the plug on the computer has failed but I am not sure exactly how to test that theory.  Do I need to bring this into a computer shop or even send it to Dell to have it looked at? Since it's way past it's warranty, not sure how much this would cost as well.

 

Thanks

Adrian