Connection issues on some clients

I'm having trouble getting some client PCs to connect to a third party application that depends on an SQL Express 2008 backend. 
Most connect OK but some throw up Connection failed / SQLState: '01000' errors. The server is up (and indeed currently in use) and all connections are from domain-connected PCs running under the same firewall Group Policies (turning the firewalls off on the server or client seems to have no effect). Different client OSs give the same error.
When I originally set the server* up for the third party to install it, I installed SQL Express 2012 (trying to be helpful) but the installer then used 2008 as that's their supported version. However, 2012 is still in place and, as far as I can tell, active on the server. Could this be part of my problem? I'm wondering if some clients are connecting to that instance of SQL instead? I don't have the knowledge of SQL to ensure all requests are going to the correct place.
Hopefully this is ...