Looking at CPAN::SQLite, it seems that the following should tell cpan not to try and load SQLite:

perl -MCPAN -e shell
cpan> o conf use_sqlite 0
cpan> o conf commit
[download]

After DBI and DBD::SQLite have been installed (again), you can try to re-enable SQLite support.

Also, you shouldn't try to mix installed modules between old and new versions of Perl in my opinion, because in the long run, some modules will fail because their XS prerequisites have only been installed for the old version of Perl.