I believe your guess is right based on my experiences from 15 years ago using MS Server 2000 and SQL Server 2000. Newer workstation clients such as Win7 are not compatible with any version of SQL server 2000;
that stuff is seriously dated, and I know for a fact that SQL server 2000 app is not compatible on anything newer than Server 2000 without upgrading the SQL server app itself.
For example, to run SQL server on MS Server 2003, you have to upgrade to SQL server 2003, MS Server 2008RT, you have to upgrade to SQL server 2008, etc. This is or at least used to be a Microsoft licensing issue. You're taking the tack of trying to solve this by applying network parameter tweaking, and that's not going to work. It's not an address, DNS, DHCP, proxy, firewall, or protocols issue. The app itself is being blocked by both a compatibility and a licensing problem.
Win7 clients were developed in 2009 which is 9 years after SQL server 2000; an eternity in programming and OS terms.
That's nearly a decade of technology advances you are trying to leapfrog with a modern windows client. Windows clients designed to work on SQL server 2000 were Win98, Win2k, and early XP beta. I'm almost certain that's not going to work. I won't go into boring tech details here; but this is the long and short of it. I'd suggest you have your Client or Company upgrade their SQL server to at least the 2003 version if not the 2008 version. As far as licensing goes, if you must have the 2008 SQL server running on a MS server 2008RT, you'll be looking at upgrading and or building a completely new core network server such as server 2008RT in order to host the SQL 2008 app on. Flat-file databases such as the Access 2007 you mentioned will work on 2008RT server without having to have the corresponding SQL server version (SQL server 2008 app) however. In fact last year on my 2008RT server, I was able to run my Access2003 database on Access2007 installed on Vista & Win7 clients connected to the 2008RT server as they don't require the SQL server app module to be installed and running on the server itself. I have no idea what server version something like Visual Studio2013 requires; you can call Microsoft and ask or a major Microsoft platinum software reseller support such as CDW or PC Mall.
Hope that helps.
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