Thanks to everyone for your responses.
Marcus and Rick, DBI and DBD::mysql are definitely installed:
[root@olive]# perldoc -l DBI
/usr/local/lib/perl5/5.8.9/DBI.pm
[root@olive]# perldoc -l DBD::mysql
/usr/local/lib/perl5/site_perl/5.8.9/i686-linux/DBD/mysql.pm
[root@olive]# perl showperlinc.pl
/usr/share/koha/lib
/usr/local/lib/perl5/5.8.9/i686-linux
/usr/local/lib/perl5/5.8.9
/usr/local/lib/perl5/site_perl/5.8.9/i686-linux
/usr/local/lib/perl5/site_perl/5.8.9
Joe, I had already confirmed that I could get into mysql from the shell prompt using the same user/password that was generating the error. But per your suggestion I went into mysql as root and did a 'grant all' to this user. Then I tried to connect via my browser, and run zebraqueue_daemon, and the same error was still present in both cases.
If it helps, here is the statement I am using in my small test script:
$dbh = DBI->connect("DBI:mysql:koha","<username>","<password>")
