So Recently I can't find any Gmod servers Nore can I do "Connect 151.80.47.13" In Console. My Internet works 100% Fine on Browsers. It Also doesn't work for other source games. All lights are on on the Connection box but it won't work on Games
If no servers work for source games what I think is happening is that there's a firewall blocking your .exe from properly accessing the internet. So if you want to fix this then you'll have to remove all permission for steam.exe's access to the firewall and then re-add them or allow the firewall to discover them again when you re-access the game.
Hope this helps!
Steam beta? Disable it.
Restart steam, I also had the same problem before where I could not find any servers.
Disable or reconfigure your firewall.
Make sure your antivirus isn't going apeshit, disable it or get a better one.