Even in Safe Mode, the same thing happens—just constant downloading. I’m reinstalling Windows XP, and even without an antivirus installed, it just starts doing it again...

I took a screenshot right after plugging in the Ethernet. It shows the netmeter I used to spot the traffic in the first place. Even a few hours after a clean install, the download is still running. Speed fluctuates from basically zero to maybe 2 Mbps, rarely hitting anything higher than that.
The OS picks up this network card without me even touching the drivers. I played around with different cards for a bit before switching back to the old one, and at first, it wouldn't recognize it—just showed that yellow exclamation mark saying the connection was limited or couldn't work. Meanwhile, my netmeter was showing active downloads happening anyway.
So, yeah... even while the connection was supposedly blocked, it was still downloading. Makes no sense...