I had tried resetting my router (which has worked in the past) but with no luck. Soon after posting this I noticed one of my other computers displaying "an IP address conflict exists with another system on the network", which reminded me of this same issue I had a few years ago. I released/renewed the IP address on that computer and my weather computer and that seems to have resolved the problem.
It's strange how this issue affects NOAA but not the Hamweather downloads.