It depends on the broadband connection that you have. Some will connect as soon as you switch on - often ADSL routers do this. Others, particularly Conexant-chipped USB connectors, don't connect until you open a window just like a dial-up modem.
You have a choice as to how you set up the internet options. One is to set it to Never dial an internet connection. If you are not connected, a box will appear telling you that you are off-line. You will then have to use the dial-up procedure to go on-line.
The other option is Dial whenever a network connection is not present. If this is set, IE will simply open if you already have a connection; if you don't, one will open and you will probably see the Verifying... box.
To change from one to the other, go to Control Panel - Internet Options - Connections and tick the relevant button.
Hi, if you want to go straight-in, one way is to use a Ethernet ADSL Modem and a pci ethernet card to attach it to. This is what I have - it is brilliant. It also has the additional security of a built-in hardware firewall. (Have a look at click here if you are interested in taking this path).