Is there a chance that the systems are different from each other? What I'm trying to say is that you may be using different versions of your ODBC library that may cause this problem. If you're using the default one, are you using different versions of the .NET Framework?
An alternative is that you may be connecting with a different user and thus attached policy? Have you tried switching the users and does that solve the issue? If that's not the case, check the URL you're using to connect if that may cause any differences.
If all is the same for all machines, you could look at the .NET Framework even though you may not be using this. For me, .NET 3.0 and beyond always were 100% successfull in connecting with any MS SQL server.