Given that (1) Winamp installed in the default [C:\Program Files\Winamp] location is launched and plays a streaming broadcast from a Web link without any problem and (2) Winamp installed in a non-default location can accept a URI and play a streaming broadcast (but not from a Web link), it seems that file associations are all okay.
Try removing Winamp (installed in the default location) entirely. Then install it elsewhere. Go to the bottom of my [
http://www.rossde.com/music.html] and select one of the speaker icons that have a Winamp icon. Does this work?