Not sure what plugins you have enabled but it could be caused by a plugin conflict.
Could you temporarily disable all the non-toolset plugins and try again ? Also if you have our Access plugin installed could you disable it as well and see if the media uploader button shows up ?
If it still does not show up, could you provide me with admin access to the page so that I can have a look at this for you?
The private fields have been enabled for your next response.