Nothing about the connection string has changed since it first worked. No port is being specified when I specify the server name (and I have done it both by IP Address and Machine Name in the past with success in either case), but right now it is using the machine name, and is not working. I tried switching it over to just the IP address, but have the same results.
EDIT: I now have it working via IP address with SQL Authentication. This did not happen before. Let me try this for a bit, and see if I can determine why it is having trouble with the machine name. If I wind up having troiuble still - I will post back.