This means that the program is attempting to reach out to the Stanford servers and download a "sub" applet that runs within the main program. Think of the core as the "formula on how to decode a protein". The core does the heavy lifting, the rest of the program is housekeeping, scoring, etc. The cores are different for different series' of proteins so it checks if you have the core for the protein it downloaded and if not, it goes and gets it.
Sounds like you were able to get the protein information, but it's failing to get the core. They come from different web servers, so one could be down BUT you had this problem earlier and I added an additional machine today and downloaded a new core no fuss no muss. I'm leaning towards a firewall or proxy issue. On the configure tab, there is a checkbox "Use Internet Explorer connection settings". Which ever way it is checked, do the opposite, close the program and start it again. That may fix it.
If it's a firewall issue, that's a little bit more complicated depending on how you're configured.