If you keep disconnecting from chat in the client, it's likely that you're experiencing network issues. This may carry into game, so make sure you don't play a game until you're successfully able to connect to chat. The Hextech Repair Tool can fix or identify several network issues for you.
Temporarily disable your firewall
If you've installed a third-party firewall, try disabling them and logging back into the client. Windows comes with its own firewall, which you can disable by following these steps:
- Click on Start
- Click on Control Panel
- Click on System and Security
- Click on Windows Firewall
- Click on Turn Windows Firewall on or off (you may be prompted to enter the Admin password at this step)
- Under each network location, select the "Turn off Windows Firewall" option
Change your DNS settings
Setting your DNS to a public domain may help if you're getting stuck getting into game. You can use the Hextech Repair Tool to do this--just check the "Automatically Assign" box.