The problem is that $sortedCollectionData only contains the indices into @collectionData, but you try to access it as if it contains the elements themselves when you try to print the data:

...
<th class=graycenter>$sortedCollectionData[$i]{'CollectionId'}</th>
...
[download]

should be

<th class=graycenter>$collectionData[$sortedCollectionData[$i]]{'Colle
+ctionId'}</th>
[download]

The deeper problem is, that your subroutine does too many things at once, which makes debugging such stuff much harder than it needs to be. I split up the subroutine into three steps, readCollectionData, sortCollectionData (where I thought the problem was) and printCollectionData (where I found the problem). That made it much easier to separate the things and see what each step returns as results.

my $orderby = 'collection';
my @data = readCollectionData('dummyFilename.txt');
my @indices = sortCollectionData($orderby, @data);
print Dumper \@indices;

printCollectionData(\@data, @indices);
[download]

As an aside, you had relatively large if ... elsif ... else ... blocks that decide on what to sort and the same kind again to translate the short status code into a long status message. I replaced them by a hash lookup:

...
    if($sortedCollectionData[$i]{'Status'} eq "I") {
      $longStatus = "Incomplete";
    }elsif($sortedCollectionData[$i]{'Status'} eq "SI") {
      $longStatus = "Submitted Incomplete";
    }elsif($sortedCollectionData[$i]{'Status'} eq "C") {
      $longStatus = "Submitted";
    }else{
      $longStatus = "Submitted Complete";
    }
...
[download]

becomes

my %translateLongStatus = (
    'I'  => 'Incomplete',
    'SI' => 'Submitted Incomplete',
    'C'  => 'Submitted',
);

...
    my ($longStatus, $rowStyle, $rowColor);
    $longStatus = $translateLongStatus{ $collectionData[$i]{Status} } 
+||'Submitted Complete';
...
}
[download]

In the end, my program looks like this (with much of the HTML printing removed):

#!perl -w
use strict;
use Data::Dumper;

sub readCollectionData {

  my $arcFile = shift;
  my (@collectionData);
  my $semaphore = $arcFile . '.lock';
  my ($longStatus, $rowStyle, $rowColor);  
    
  #open(LOCKFILE, ">>$semaphore") or die "$semaphore: $!";
  #flock(LOCKFILE, LOCK_EX) or die "flock() failed for $semaphore: $!"
+;
  #open (ARCFILE, "<$arcFile") or die "Failed to open $arcFile: $!";
  local *ARCFILE = *DATA;
   
  # Retrieve file information from arcFile as an array of hashes
  while( <ARCFILE> ) {
    my( $col, $cnt, $stat, $miss, $mod) = m[
        ^
        CollectionId \s* => \s* (\d+)? \s*
        Framecount \s* => \s* (\d+)? \s*
        Status     \s* => \s* (\w+)? \s*
        Missing    \s* => \s* ([\d,]+)? \s*
        Modified   \s* => \s* ([\d/]+\s[\d:]+)? \s*
        $

    ]x or warn "Bad format at line $.\n" and next;

    my( $modday, $modmon, $modyear, $modhrs, $modmin, $modsec ) = 
        $mod =~ m[(\d+)/(\d+)/(\d+) (\d+):(\d+):(\d+)]
        or warn "Bad date format in line $." and next;

    push @collectionData, {
        CollectionId => $col,
        Framecount => $cnt,
        Status => $stat,
        Missing => $miss,
        Modified => sprintf( "%4d/%02d/%02d %02d:%02d:%02d",
            $modyear, $modmon, $modday, $modhrs, $modmin, $modsec ),
    };
  }
  return @collectionData
};

# Map the program orderby names to the internal names in the hash
my %sort_columns = (
    collection => 'CollectionId',
    framecount => 'Framecount',
    status     => 'Status',
    missing    => 'Missing',
);

sub sortCollectionData {
  my ($orderby, @collectionData) = @_;
  # Sort the collection according to orderBy param
  
  my $sort_col = $sort_columns{ $orderby } || 'Modified';
  
  my @sortedCollectionData = sort {
    $collectionData[ $b ]{$sort_col} <=> $collectionData[ $a ]{$sort_c
+ol}
    ||
    $collectionData[ $b ]{Modified} cmp $collectionData[ $a ]{Modified
+}
  } 0 .. $#collectionData;
  return @sortedCollectionData
}

my %translateLongStatus = (
    'I'  => 'Incomplete',
    'SI' => 'Submitted Incomplete',
    'C'  => 'Submitted',
);

sub printCollectionData {
  my ($collectionData, @sortedCollectionData) = @_;
  my @collectionData = @$collectionData;
  my $transactions = scalar(@collectionData);
  for (my $i=0; $i < $transactions; $i++)
  {
    my ($longStatus, $rowStyle, $rowColor);
    $longStatus = $translateLongStatus{ $collectionData[$i]{Status} } 
+||'Submitted Complete';
 
    if (($i%2) == 0){
      $rowStyle = "oddrow";
      $rowColor = "#e5e5e5";
    }
    else {
      $rowStyle = "evenrow";
      $rowColor = "#ffffff";
      
    }
    print $i, $longStatus, $collectionData[ $i ]->{CollectionId}, "\n"
+;
  }
}

my $orderby = 'collection';
my @data = readCollectionData('dummyFilename.txt');
my @indices = sortCollectionData($orderby, @data);
print Dumper \@indices;

printCollectionData(\@data, @indices);

__DATA__
CollectionId=>26154 Framecount=>6 Status=>SC Missing=>0 Modified=>01/2
+2/2012 22:12:09
CollectionId=>26155 Framecount=>6 Status=>I Missing=>4 Modified=>01/22
+/2012 22:12:20
CollectionId=>25000 Framecount=>6 Status=>SC Missing=>0 Modified=>01/2
+2/2012 22:13:07
CollectionId=>25002 Framecount=>6 Status=>I Missing=>5 Modified=>01/22
+/2012 22:13:14
CollectionId=>25009 Framecount=>6 Status=>I Missing=>5 Modified=>01/22
+/2012 22:13:19
CollectionId=>25309 Framecount=>6 Status=>I Missing=>5 Modified=>01/22
+/2012 22:13:25
CollectionId=>25349 Framecount=>6 Status=>I Missing=>5 Modified=>01/22
+/2012 22:13:31
CollectionId=>25318 Framecount=>6 Status=>I Missing=>5 Modified=>01/22
+/2012 22:13:37
CollectionId=>21318 Framecount=>6 Status=>I Missing=>5 Modified=>01/22
+/2012 22:13:43
CollectionId=>21342 Framecount=>6 Status=>I Missing=>5 Modified=>01/22
+/2012 22:13:56
[download]