Late 2007 Black MacBook will not charge with L-Shaped Adapter

I have a Late 2007 Black MacBook and I am having trouble charging the device. I have been having an issue with the original 60W T-Shaped Adapter LED glowing very faintly then not at all. So I bought a new 60W L-Shaped Adapter and it charged the MacBook fully. However, it will not charge the MacBook any more but the T-Shaped Adapter now has started working again with the laptop.

I checked the SMC firmware update for this model and when I tried to install that, it said the firmware was not required. The reason I tried to install that was an article on Apple's support site.

Has anyone else noticed issues with the Black MacBook and charging? The battery shows Normal.

I have tried an SMC Reset.

Any ideas? Being that the T-Shape is now working but the L-Shape is not I am confused since the L-Shaped worked once.