I bought this PC 2 months ago. Yesterday, I had to transport it by car. Even though I packed it in the original box with foam, when I tried to set it up again, I noticed that this cable, which I had secured with electrical tape, was loose. I'm sure it wasn't loose before.
I know it's some kind of power cable, but I don't know where to plug it in (I'm not a hardware guy).
Note: The PC is turning on and functioning normally. I don't know if it's related or just a coincidence, but my headphones that I usually connect to the back stopped working.
It looks like a fan header with a molex split. But more pictures would be needed to confirm 100% (A picture of where the cable connects to the motherboard in particular)
My guess is that the molex end was never connected to anything and was simply tucked under the IO shield to the left or the VRM heat sink above. It was probably jostled loose during transport. You can take a look around for anything with the same size as the loose connector to see if something was plugged in there. The connector is shaped like the letter "D" where one side is flat and the other has slightly rounded corners so you can only plug it in one way. This cable is for power only so it would probably be something like a fan or a light.
If I am correct then the cable can be left unplugged and you can tuck it somewhere to hide it or just leave it taped. It would also be unrelated to your headphone issue.