Thank you all! I got some great ideas from that - I eventually used a while loop though:

#!/usr/bin/perl -w

print "Content-type: text/html\n\n";

use CGI::Carp qw(fatalsToBrowser);

opendir(DIR, ".");
@files = grep( /\.tmp/, readdir(DIR) );
@files = sort(@files);
closedir(DIR);

foreach $file(@files){
$found = 0;
open(FOO, "$file") or die "Cannot open. $!\n";
while (<FOO>){
print "Copying table from $file...<br>";
if ( $_ =~ m/<!--TABLE -->/ig){
$found = 1;
}
if ($found == 1){
open(FILE,">>filename2.txt") or die "Cannot open. $!\n";
print FILE $_;
close(FILE);
}
if ( $_ =~ m/<!--\/TABLE -->/ig){
$found = 0;
}
}
close FOO;
}
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