Vista was the first Windows OS to deploy with the "broadcast flag" enabled (long articles what it is, what trouble it caused and more on the web) so forget WiFi for a bit and let the machine fetch all Windows Updates over Ethernet (wired) and see if your router firmware is current.

I do not want to explain this flag here. It's rather overdone so I'll refuse to duplicate all that (so many balked and had to be dragged to the well) and head to what I used to fix it.

In short, router firmware shall be current, use Ethernet until that is done and you still have the old PC issue. It could be broekn.