Thank you, Neemobeer. I've solved the issue.
I opened Resource Monitor (search "resource"), and opened the network activity. At fist I thought it was Avast, because it (instup.exe) kept trying to update itself, I went to update it manually. No problem.
Then I saw a process called SVCHOST.EXE (NETWORK SERVICE), with its address "CACHE.GOOGLE.COM". I went and cleared Google Chrome's cache, cookies etc. and the problem was solved! I restarted, opened my Internet USB, connected, without opening a page, and it did nothing, just stayed quiet, no downloading, nothing.
It appears that something in the Google Chrome cache, was still downloading something.
Thanks for all the advice!