SELECT $columns, COUNT(PdbID) as c GROUP BY PdbId HAVING c >= 2
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++moritz for the idea of succinctly expressing this in SQL. (I will address it in Perl in a later post).

Perhaps I read the OP differently, but I think that this SQL, as given, will not produce the desired results.

Here is my test setup, using SQLite (tested on Win32 and Linux):

sqlite3 PM_617794.db
DROP TABLE IF EXISTS pdbs;
CREATE TABLE pdbs(
  PdbId       TEXT,
  MetalAtm    TEXT,
  MetalName   TEXT,
  MetalNumber INTEGER,
  MetalChn    TEXT,
  AtmName     TEXT,
  ResName     TEXT,
  ResNumber   INTEGER,
  ResChn      TEXT,
  Distance    NUMERIC
);
INSERT INTO pdbs VALUES('1nc7','MG','MG',1501,'-','CL','CL',1401,'-',3
+.065);
INSERT INTO pdbs VALUES('1nc7','MG','MG',1501,'-','CL','CL',1402,'-',2
+.660);
INSERT INTO pdbs VALUES('1pex','CA','CA', 503,'-','CL','CL', 501,'-',2
+.895);
INSERT INTO pdbs VALUES('1qhu','NA','NA',   3,'-','CL','CL',   1,'-',3
+.096);
INSERT INTO pdbs VALUES('1qjs','NA','NA', 513,'A','CL','CL', 511,'A',3
+.096);
INSERT INTO pdbs VALUES('1rtg','CA','CA',   2,'-','CL','CL',   1,'-',3
+.079);
INSERT INTO pdbs VALUES('1xj6','NA','NA',5002,'-','CL','CL',5001,'-',2
+.628);
INSERT INTO pdbs VALUES('2caj','NI','NI',1151,'B','CL','CL',1150,'B',3
+.551);
INSERT INTO pdbs VALUES('2oa9','CD','CD', 911,'-','CL','CL', 800,'-',2
+.291);
INSERT INTO pdbs VALUES('2oa9','CD','CD', 913,'-','CL','CL', 801,'-',2
+.403);
.mode column pdbs
.width 4 2 2 4 1 2 2 4 1 5
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Here is your query, with the FROM clause added, and the $columns resolved to '*':

SELECT   *, COUNT(PdbId) as c
FROM     pdbs
GROUP BY PdbId
HAVING   c >= 2
;
[download]

Output:

1nc7  MG  MG  1501  -  CL  CL  1402  -  2.66   2
2oa9  CD  CD  913   -  CL  CL  801   -  2.403  2
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There are two problems here:

1. Any GROUP BY clause can produce only *one* record per unique grouped-by field. The OP needs *all* the records which have groupings of more than one record. To achieve this, you must either use
   1. a sub-Select, or
   2. two Selects with a temp table storing the results of the first Select for use by the second Select.
   I don't see how it can be done with a single simple Select.
2. Your SQL would produce a record if a PdbId had two records of *any* values of ResName. The sample data does not happen to have this scenario, but the code should not depend on that. The issue can be resolved by
   1. filtering with a WHERE clause; WHERE ResName = 'CL', or
   2. (more maintainably and flexibly) by adding ResName to the GROUP BY clause, and also filtering with WHERE.
   The OP *could* be read as using CL only as a representative of matching values; if so, then the WHERE is not needed, but the addition to GROUP BY becomes mandatory.

Here is your SQL, modified as 1a and 2b above:

SELECT     pdbs.*
FROM       pdbs JOIN (
  SELECT   PdbId, ResName, COUNT(*) as c
  FROM     pdbs
  GROUP BY PdbId, ResName
  HAVING   c >= 2
) AS       counter
ON         pdbs.PdbId   = counter.PdbId
AND        pdbs.ResName = counter.ResName
WHERE      pdbs.ResName = 'CL'
;
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Outputs:

1nc7  MG  MG  1501  -  CL  CL  1401  -  3.065
1nc7  MG  MG  1501  -  CL  CL  1402  -  2.66
2oa9  CD  CD  911   -  CL  CL  800   -  2.291
2oa9  CD  CD  913   -  CL  CL  801   -  2.403
[download]

Here is a solution in Perl.

Working, tested code:

use strict;
use warnings;

my @field_names = qw(
  PdbId   MetalAtm MetalName MetalNumber MetalChn
  AtmName ResName  ResNumber ResChn      Distance
);
# Trick for concise sample data.
sub aref_to_href {
  my @field_values = @_;
  die unless @field_names == @field_values;

  my %h;
  @h{@field_names} = @field_values;

  \%h;
}

my @records_AoH = map { aref_to_href( @{$_} ) } (
  [ qw( 1nc7 MG MG 1501 - CL CL 1401 - 3.065 ) ],
  [ qw( 1nc7 MG MG 1501 - CL CL 1402 - 2.660 ) ],
  [ qw( 1pex CA CA  503 - CL CL  501 - 2.895 ) ],
  [ qw( 1qhu NA NA    3 - CL CL    1 - 3.096 ) ],
  [ qw( 1qjs NA NA  513 A CL CL  511 A 3.096 ) ],
  [ qw( 1rtg CA CA    2 - CL CL    1 - 3.079 ) ],
  [ qw( 1xj6 NA NA 5002 - CL CL 5001 - 2.628 ) ],
  [ qw( 2caj NI NI 1151 B CL CL 1150 B 3.551 ) ],
  [ qw( 2oa9 CD CD  911 - CL CL  800 - 2.291 ) ],
  [ qw( 2oa9 CD CD  913 - CL CL  801 - 2.403 ) ],
# Added for testing different ResName columns
  [ qw( 99zz CD CD  911 - CL YY  800 - 2.291 ) ],
  [ qw( 99zz CD CD  913 - CL YY  801 - 2.403 ) ],
);

my %count;
$count{ $_->{PdbId} }{ $_->{ResName} }++ foreach @records_AoH;

# Uncomment the second `grep` line if needed.
# (See the SQL discussion in the previous node).
my @filtered_AoH = grep { $count{$_->{PdbId}}{$_->{ResName}} >= 2 }
#                  grep { $_->{ResName} eq 'CL' }
                   @records_AoH;

my $template = '%5s %8s %9s %11s %8s %7s %7s %9s %6s %8s';
printf "$template\n", @field_names;
foreach (@filtered_AoH) {
  printf "$template\n", @{ $_ }{@field_names};
}
[download]

PdbId MetalAtm MetalName MetalNumber MetalChn AtmName ResName ResNumbe
+r ResChn Distance
 1nc7       MG        MG        1501        -      CL      CL      140
+1      -    3.065
 1nc7       MG        MG        1501        -      CL      CL      140
+2      -    2.660
 2oa9       CD        CD         911        -      CL      CL       80
+0      -    2.291
 2oa9       CD        CD         913        -      CL      CL       80
+1      -    2.403
 99zz       CD        CD         911        -      CL      YY       80
+0      -    2.291
 99zz       CD        CD         913        -      CL      YY       80
+1      -    2.403
[download]

PdbId MetalAtm MetalName MetalNumber MetalChn AtmName ResName ResNumbe
+r ResChn Distance
 1nc7       MG        MG        1501        -      CL      CL      140
+1      -    3.065
 1nc7       MG        MG        1501        -      CL      CL      140
+2      -    2.660
 2oa9       CD        CD         911        -      CL      CL       80
+0      -    2.291
 2oa9       CD        CD         913        -      CL      CL       80
+1      -    2.403
[download]