Try this https://dl.dropboxusercontent.com/u/93545993/VACAF2.3.zip
That's a .exe someone made that tries a handful of fixes specifically for the VAC authentication error. It looks like it was made more for CS:GO but I would assume it would work on TF2 considering a lot of the troubleshooting tips are the same for different VAC protected games.
Have you tried rebooting your router?
Those didn't work either....Had this error too. I opted into steam beta and back out of it and it was miraculously gone. Maybe that procedure could help you too. Good luck!