Barrel Port Broken, USB-C Charging Working

A while ago, my barrel charging port broke on my XPS 15 9560. It worked for a day by jiggling the plug around a bit before quitting altogether. I set up a support ticket since I still had a premium warranty, and they wanted me to send the laptop in for them to fix it.

I then needed to use my laptop for work, so I got the ticket put on hold and bought a USB-C charger. (45W) It started charging when I plugged in the USB-C charger. A few weeks later, I sent in the laptop with the 130W barrel charger from Dell to get the barrel port fixed as it's much more useful since it can use the 130W adapter.

They told me the battery needed to be replaced. I told them not to fix the battery since I knew the battery itself was still functional, and it was outside the warranty. When I received the laptop back, the barrel port still didn't work and the USB-C port still did work. They told me they just replaced the cord that goes from the wall outlet to the 130W adapter brick.

I called and asked why the port hadn't been fixed, and they said the problem was with the battery and not the port. I do not understand how this could be. I also asked what the battery test had consisted of and why it needed replacing, but I could not get an answer outside of "The battery failed the test."

So my questions are:

What does Dell's battery test consist of?

How could the battery 'being bad' break the DC port and not the USB-C port? Does the battery have separate pins to charge from the different ports?

If it's not the battery, is it likey the port on the circuitry connected to the port? Would there be a way to test which it is? And finally, if it is the port, can a replacement port be bought?

Thanks to anyone who actually got through all that, and thanks to anyone who can help!