The problem is probably with the ODBC configuration on the Server itself. In other words the connection string [to the ODBC source] is ok (since tested on other server), but it makes reference to a source that is not configured on this particular server.
To remedy the problem, open the ODBC Data Source Administrator (typically one of the shortcuts in the "Administrative" tools menu), and check if indeed you have a source (typically a "System DSN") with the same name found in the connection string. Such Source is probably inexistant or improperly configured.
Aside from performance considerations, one may consider using more direct Data Providers (such as MS SQL Data Provider or Microsoft.Jet.OLEDB) at the level of the connection string; this avoids the extra configuration point (the ODBC config panel) on the server (but then this may require using two distinct connections strings, one for the test environment and one for the production environment...)
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