I'm trying to manually install the DBI module from CPAN ... After I downloaded the zip file in CPAN ...

Why are you trying to do that all that manually? Strawberry Perl comes with its cpan utility which (the last time I used it) involved a command line like
    cpan install Module::DBI
(Update: Sorry, should have checked first. Actually, at the Windows DOS command prompt, type
    c:>cpan
to start the Strawberry cpan shell, then at the shell prompt type
    cpan> h
for "help" info. "install" is what you're looking for.)
to do the dirty work.

When I typed in C:>cpan Module::DBI ... "Warning: Cannot install Module::DBI, don't know what it is"

I don't see any Module::DBI module on CPAN (actually MetaCPAN now); are you sure this is really the name of the module?