You have no problem using your modem to connect to your ISP.

After you disconnect, you cannot reconnect until you restart your computer. When you try, you receive error 619.

You are probably using a 3rd-party firewall or network utility that is NOT releasing the Winsock stack.

Contact the 3rd-party software provider and ask about a fix.

To workaround this behavior, uninstall the 3rd-party software.