# first attempt
...
my $start = time;
my $dbh = DBI->connect("DBI:SQLite:$dbfile") or die;

my $sth = $dbh->prepare( qq(INSERT INTO 'logentries' 
    ('col1', 'col2', 'col3', 'col4') values (?,?,?,?) ));

$sth->execute($_->[0], $_->[1], $_->[2], $_->[3]) for @rows;

print "et: ", time - $start, " sec\n";  
# et: 1082 seconds

##</code><code>##

# single transaction
...
my $start = time;
my $dbh = DBI->connect("DBI:SQLite:$dbfile") or die;

$dbh->do('BEGIN');

my $sth = $dbh->prepare( qq(INSERT INTO 'logentries' 
    ('col1', 'col2', 'col3', 'col4') values (?,?,?,?) ));

$sth->execute($_->[0], $_->[1], $_->[2], $_->[3]) for @rows;

$dbh->do('COMMIT');

print "et: ", time - $start, " sec\n";  
# et: 5 seconds