What should I check first?

End of cable that connects to PC? Other end of this same cable connecting to the power supply? The connection where the power supply is connecting to outlet? (Not the cord itself but inside of the supply)

If someone could give me the proper terms, or a better way to describe these items I'd appreciate it!

I just acquired this AC adapter and quickly realized the LED indicator on the unit would not light up when plugged in.

I removed the case for power supply, did some wiggling and when I plugged it back in the LED indicator came on.

After doing this, I attempted to plug it into the PC. Shortly thereafter the LED went off again. I did not initially notice that the end that connected to the PC had seeming exposed wire (looked like tubing got pushed back).

Could the AC Cable Adapter Outlet (How to Repair a Frayed Dell AC Adapter Cable) result in the LED not lighting up on the power supply?