I would check the workstations for any lingering pointers to the old server in the registry, configuration files, or anything that could reference a mapped drive.
We had a problem very, very similar. Installed new accounting software on a new server. Installed new accounting client software on all PC's in accounting and pointed to the new server. After 3 weeks everything was running smoothing, so the old accounting server was shutdown. Immediately everybody started complaining and slow response. A couple of the server guys installed the client software on their PC's and they were fine. The server and the server guys were on the same floor, but the accounting people were on a different floor. So of course it was a network problem. After spending a few hours of looking, the networking group (me) found the PC's in accounting were attempting to access the old accounting server, which was down.
Registryand configuration files were cleaned, performance went back to normal.