Hello again FIP
I got home tonight and thought more about what you wrote and tried getting Live365 on a different computer - one that just had IE 7.0 and no associated music player on it.
I hope that you can see the screen shot I took, which should be below. One thing I did was to flush the browser cache - you can do this by going to Tools, then Internet Options (this is for IE) - then just click on the button to delete all temporary records and files - this helps sometimes, but I'm certainly not going to say this is your system's problem, since this is only my guess.
I was able to get the radio working after I signed in. I hope you let us know some more details when you have time - I'm sure there are many others far better suited to help you than I, but that doesn't stop me from trying!
Have a good night!
PS - I just found this - perhaps it might also help:
http://www.live365.com/help/listen/windows/index.html
Attached Image. (Click thumbnail to expand)