I recently had the misfortune of having some really old Server 2000 and Server 2003 boxes thrown my way that needed patching, and Windows Update was not loading in Internet Explorer 6 when it should have. Both servers gave slightly different error codes, but ultimately the rather quick fix was to go into Internet Explorer, and in the tools menu, into internet options. The in the advanced tab, under security, make sure that TLS 1.0 was enabled, which in the case of these two servers was not.
For good measure I also disabled SSL 2.0 and 3.0, as those really should have been turned off by now. after this was done, a quick restart of the browser allowed me to get to Windows Update again.