If the power just shuts off when you disconnect the power adapter, then maybe the battery is just no good, and doesn't accept a charge now.
Do you know how old the MacBook is? If this is an older MacBook (white or black case, not aluminum), then you can check the serial number label inside the battery compartment, which will tell you the processor speed, and a few other items about the original configuration. The processor speed would tell a lot. Maybe you know the exact year of the MacBook...
In those older MacBooks, you can press the battery test button on the battery. If the battery has no charge at all, no lights will illuminate when you press the test button. Plug the power adapter in, and wait about five minutes, then check if ANY lights will come on. If you don't see any lights, even after the power adapter is plugged in for several minutes, then the battery probably needs to be replaced (if your friend wants to use it as a portable again), or possibly the battery connector cable can be bad (it's an internal cable where the battery connects), or the Magsafe card can be bad, too, letting power in, but won't charge the battery. So, lots of possibilities. You can get a better check on the battery if you can boot to a system. OS X on an external drive, then go to the power information in the System Profiler (System Information with Lion or later)