Chatting, unlike most commands, does not usually 'bounce' any information back to your client. While chatting may appear to be running full speed on your end it could be just as lagged as the commands you are issuing.
Perhaps a script or virus is flooding the server with data and causing the server to throttle all of your input. Use /debug -p @debug to see what you are sending to the server. It is a bit weird if you are testing on both dialup and broadband from the same computer (and to the same server) though.
Hope that helps