So, I just reinstalled TF2.
When I try to start it, it starts in a window, but does not show the window border.
It shows the Valve logo, and when the "Powered by Source" screen fades away, the window just closes at once and shows the Steam update news.
I instructed Windows Firewall to allow TF2 to run as it needs to, but yet, it still has the same results.
Help?