Thank you for your answer, Big Dan.
I'm using Windows Vista; I put that in my original post, but when I asked to preview it, I was told that I wasn't signed in, although I was, and so I lost the whole post. Then I obviously forgot to mention which system I use when I re-wrote it
The Hotmail icon I'm talking about is the Windows Live Messenger icon of two figures in a square, one green and one blue, with a yellow ribbon around them. When I'm off-line, it has a red cross on it. Clicking on it brings up the attached picture where I currently have 10 hotmail addresses memorised - yes, they do need sorting out!
With Vista, it is on a taskbar at the bottom of the computer screen. I would go and look at the family PC, which has Windows XP, but it takes hours to get going
We did use to have the same icon on there, but I think it was on the main screen (desktop? I'm sorry, but I'm a total technophobe and don't even know the proper lingo) but that one disappeared a while ago, perhaps when Hotmail started their social networking campaign.
I do have some very good news for my computer.
After posting my message, I turned it off, didn't use it for a couple of days and found that, during its beauty sleep, it had regained its Hotmail icon
So that problem is solved - apart from where it went to
However, having brought up the subject, it would be really great to find a way to get the same icon back for the family PC.