Sorry that I'm answering on an off-topic question, but I would like to help immediately since it's serious and he needs help. (if you want me to delete it, please post a comment!)
I have searched for a way to download files without a browser, and I hope it will work for you. Open up your Powershell and use this code:
(New-Object System.Net.WebClient).DownloadFile("htts://www.testadress.test","file.exe")
Better paste the code in a notepad window before and edit the address to a real one pointing to a file. Note, the file is going to be always called file.exe if you don't change it.
Some reliable programs to remove unwanted files and viruses are below. Hopefully you are able to check the download links by yourself, because it seems to be hard to find static links quickly.
There is a collection full of interesting software tools called GeGeek Tech Toolkit. It contains tools which are very useful for cases like these, but the most recent versions became paid donationware. Here is one source for an older version, sorry that it's not English: http://www.chip.de/downloads/GEGeek-Toolkit_71776498.html - For a translation, copy and paste the URL in the form here: https://translate.google.com
In this collection there is a folder called "Repair Tools" with many programs and fixes. Hopefully one of it with help you to fix your nasty internet issue.
Last, try a scan for corrupted Windows files. Open a command prompt with admin rights (cmd.exe), and type this: sfc /scannow
I wish you good luck!