If the download from cpan.org is perl then it is usually a core module. I just clicked the dependencies link from cpan.org for this module and it states there that it is a core module. So no need to install the module. As I asked in a previous post have you installed the software gdbm for windows? You said this was all working on a previous machine: what os was that machine? Was gdbm for windows working on that machine?
The first thing it states on the cpan page for this module is
GDBM_File - Perl5 access to the gdbm library.
That means this is a wrapper module that lets you access gdbm. The page goes on to tell where to download gdbm which means it is something separate from this module.