For organizational reasons, I renamed a DotNetNuke 4.3.5 installation:

(old name)
System Directory: c:\DNN\test\
Application Name/Virtual Directory: dnn_test

(new name)
System Directory: c:\DNN\live\
Application Name/Virtual Directory: dnn_live

Besides renaming the system folder and the IIS Virtual Directory Application Name, I also reattached the SQL Server Express based database (now in its newly renamed folder) and I modifed the Home Directory > Local Path setting in IIS for the domain that uses the renamed DNN installation. After the renaming, the portal works great except for the Repository module.  There are images in this particular repository, alongside notes.  The notes display fine, but the images will not render.  When you click a missing image (X) indicator, it tries to resolve to the old application name (dnn_test).

Could someone suggest where I might find the old application path that is embedded in the repository module that points to the image objects?  I hope to manually update that path and keep the new naming convention.

Since I only have one instance of the Repository Module in this portal, all I needed to do - as you suggested - was to login as HOST and change the path(s) listed in:

Repository Module > Settings > Repository Settings:

Folder for Approved Files
Folder for Unapproved Files
Folder for Anonymous Files

... and the images displayed once again.

You got right to the heart of the problem, Mike.  Thank you.