Chosen Solution

My MacBook Air power cord seems to be breaking inside the cable. How can I repair it? Thanks.

Using an exacto knife cut the cable length wise. Some were there should be a loose wire just solder it together.Now you can tape the outer sleeve back or make one out of duct tape (which should be god for all creators). -Me-

Check my guide MacBook Power Cord 5-Pin MagSafe Connector and Cable Replacement

One of the two cables might have broken off of the pcb inside the main housing of the power adapter. The cables have crimped ends which can break due to cable-movement, causing erratic loading/not loading although the light is constantly on.