G-CPTN -- my trusty old laptop is using Vista Home Premium+IE8 and when I go to NASA.gov and click on Multimedia and select NASA TV from the drop-down menu, the TV starts no problem.
Have you got the latest JAVA and Flash plugins installed? I remember recently I was trying to load a site which wouldn't play and it turned out that I hadn't got the latest Flash player... just go to the Sun Java site and check.. it may just be that you need a more recent version?
I shall cross fingers that that works :-)