It turns out that the problem was more of a Microsoft Windows security settings issue. Our new server has a Windows Server 2008 R2 operating system (old server - Windows Server 2003). There's some setting(s) or lack thereof that is preventing the recognition of the "Database Connections" part of the db connection path when accessing via a python script. Haven't resolved that yet but with the help of Umesh from ESRI tech support, I have a workaround that is described below:
Instead of specifying the db connection as "Database Connections\sde_loader@bierstadt.sde"
Obtain the path name on the C drive by right clicking the db connection in ArcCatalog and selecting properties. The path name is on the General tab.
In my case, the name is: C:\Users\ehrhardt\AppData\Roaming\ESRI\Desktop10.1\ArcCatalog\bierstadt_saxon2.sde
Inserted this name into the script, and the script finally worked!
Thank you to Matthew & Wayne for your suggestions and to Umesh for the workaround solution.