"Error establishing a database connection" message

Up until some three weeks ago, the blogs system in my BP multisite, 1.2.8 version, was working properly.

Recently, however, blogs are not working as they should. When one creates a blog, the system indicates it was created, but then when one clicks on the blue string the system automatically creates to access it (and start posting), there is an error saying, "Error establishing a database connection".

I contacted my host, Godaddy, where we have a virtual dedicated server, and their server support technicians indicated that mysql server is working fine. The problem I was told, is related to the connection strings with the server, which need updating.

If there is nothing else to be done to cope with the problem, other than this updating, does any one knows how to update the connection strings with the mysql server? Is there a relevant link to which you may point us where the solution to the problem is described? Is there some kind of standard procedure to examine and updating such connection strings if something of a similar nature happens in the future?