Recurring Problem Getting On-line

I'm not sure if this is one problem or two or more, but I'll try to explain what's happening.

When I turn on or wake up my computer and click on the little internet icon with the yellow triangle in the very bottom right of my screen, a window will appear. In this window I click on "Connect to Broadband Network" as I've always done and then click "Connect". A second window appears with my username and password where I again click "Connect". At this point three more little windows briefly appear and disappear and I'm supposedly connected. So far, so good, except for the fact that the little yellow triangle in the bottom right is still there. If I mouse over the icon it shows "No Internet Access", but if I click on it, the first window appears and says that I am connected. Now, if I just go ahead and click on IE in the lower left (taskbar), Internet Explorer displays that I'm not connected to the internet. If I close IE, then click on the icon in the lower right again, then click "Disconnect" and repeat the entire process all over again, I may get on the internet, but quite often it takes three tries. Usually, on the second try, the little yellow triangle will be gone, showing that I now have "Internet Access", but IE will show "Can't Display the Page" message. As I said, the third time around it usually all works.

You can try run devmgmt.msc - expand Network Adapters - right click the network card and go into properties - switch to the Power management - uncheck Allow the computer to turn off this device to save power. This shouldn't cause any problems if you are properly shutting down the PC though afaik, perhaps you are hibernating/sleeping the PC?