Network System tray Icons

My Windows 7 system sometimes shows the System tray network icon (or the same with a red cross on it), and at other times it shows .

What do these icons mean?

In both cases, if I hover over the icon it says I've got an internet connection...

Thanks - Rowan

First one is a wired connection icon and the next is wireless connection with the bars.

Thanks for your reply.

In that case, it's broken then, because I never have a wired connection. Sometimes it must be failing to recognise that it's connected wirelessly. Why would that be? Would it have any adverse consequences, or help to explain any of the odd things that now and again happen to me (blue screens, hangs, things going unbelieveably slowly etc.)?

What does the "wired connection" with a red cross on it mean? When this happens I still see "Internet Access" if I hover over the icon (and I normally do have internet connection).

Thanks - Rowan

Rowan. Sounds like you have some conflicts going on. Have you tried a system scan. If not have a look at this tutorial. http://www.sevenforums.com/tutorials/1538-sfc-scannow-command-system-file-checker.html
You may also need to have a look at
http://www.sevenforums.com/crashes-debugging/96879-blue-screen-death-bsod-posting-instructions.html
This can get you started at solving your Blue Screens and hangs.