Can't find my external data source when add new external content type

So, I've logged into SharePoint 2010 Designer and went to go add a new external content type. I'm only connecting to one external database, so when I click to discover external data sources and define operations, I don't see my external data source.  I attempt to do a search and it doesn't find anything, so then I manually add it.  This doesn't work, because it then adds another data source to my BDC.

The funny thing is that my other content types from the same source are still working.  I had read online that if running into the problem I explained earlier that you try to edit a method on an existing external content type and that should reestablish connection to your data source.  I did that and SP Designer tells me that it can't connect to the data source.  Here's where everything gets really crazy.

A couple of months ago, my infrastructure team had to change the IP address of the database server that I was connecting these external content types to.  Since this database server was external to our domain, I couldn't connect to it with a fully qualified domain name, only by IP.  When the edit operation fails, I'm presented with a dialog for the SQL connection.  Everything is fine with the connection except for the Database Server IP address, which is still the old address of the server. 

I'm not sure if all of this is related, but I really need to get this new content type deployed and I'm at my wits end.