I suspect you are not on an "always on" connection with your ISP (Who is it?) When you click the connect button to start your modem it goes through a "Training Mode" (Perhaps amber icon before it goes green) whereas your IE is already looking for the homepage which it can`t find in the timeout period set in IE. Therefore the page is blank. By the time you refresh the page the connection has been made.
If you start the modem connection first and then open IE you`ll get it immediately. I don`t think there is a way to get round this. It should only be perhaps 10-15 seconds at most. What type of modem is it?