Um, I'm hoping your cutnpaste lost something, but there's trouble between the open(FilesToGet, ' and the {, as it might be:

open(FilesToGet, "FilesToGet.txt") 
  or die "can't open FilesToGet.txt: $!";
while (<FilesToGet>) {
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and then you can skip

$TheFile = $_;                         
    chomp($TheFile);                 
    $INFILE = $TheFile;
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and just do:

chomp;
$ftp->get($_);
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but to make life even easier:

#!/usr/bin/perl -w
use Net::FTP;
use strict;

my $hostname = 'user defined';
my $username = 'user defined';
my $password = 'user defined';
my $home = 'user defined';
my $debug = 5;
 
open(FilesToGet, "FilesToGet.txt") 
  or die "can't open FilesToGet.txt: $!";
my $ftp = Net::FTP->new($hostname);
$ftp->login($username, $password);
$ftp->cwd($home);
while (<FilesToGet>) {
  print STDERR "Getting $_" if $debug > 3;
  chomp;
  $ftp->get($_);
}
$ftp->quit;
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a