Recently one of my friend was having problem of not displaying Silverlight content on his Firefox, while he was able to view it in IE. The problem was an addon. If you are one of those who have installed Silverlight, but still getting "Get Microsoft Silverlight" Button in Firefox then you should check if one of these is causing it :
It may be one of the Firefox addons you have added which is causing this, you should check that. Most common is the Flashblock addon or it can be Mediawrap addon. So disable these or such similar addons from Firefox. Goto Tools > Add-ons to get the list and disable it.
Then restart Firefox and now you will be able to view SIlverlight content.
Another reason may be, check whether SIlverlight is disabled , for this type "about:plugins" in FIrefox address bar & check the list. So reinstall it.
Now you can view Silverlight content on your Firefox also.