Cutting a long story short, something is blocking you connecting to TCP Port 6667, which these game need. Some providers block that as a matter of course (yours does not as far as I know) but many institutional providers do. Are you connecting from an institution? It is still something of a mystery why it worked and then stopped working.
If you have Windows 10, please could you open Windows Power Shell (type "Power Shell" at the start menu) and in the shell type this
Test-NetConnection peerchat.server.cnc-online.net -port 6667
and then post the result in here.
Please could you also open a command prompt (type "Command Prompt") at the start menu and in the dos shell type "IPCONFIG" and post the output in here.