Show us runnable sample code that demonstrates the problem. Note that template loops with nested data require a nested data structure so your sample code should show us how you create that structure. Most likely you want something like:

use strict;
use warnings;
use HTML::Template;

my $html = <<HTML;
 <TMPL_LOOP NAME="files_loop">
   <tr id="TMPL_VAR ID>">
     <td><TMPL_VAR NAME ="index"></td>
     <td><TMPL_VAR NAME ="filename">   </td>
     <td><input type="checkbox" name="field" <TMPL_VAR NAME="check">>
     </td>
   </tr>
</TMPL_LOOP>
<form action="index.cgi" method="post">
    <input type="submit" name="Edown" value=" Download ">
    <input type="hidden" name="cmd" value="download">
</form>
HTML

my $tmpl = HTML::Template->new(scalarref => \$html);
my @loopParams = (
    {index => 1, filename => 'plonk', check => 'f1'},
    {index => 2, filename => 'pip',   check => 'f2'}
    );

$tmpl->param(files_loop => \@loopParams);
print $tmpl->output();
[download]

prints:

 
   <tr id="TMPL_VAR ID>">
     <td>1</td>
     <td>plonk   </td>
     <td><input type="checkbox" name="field" f1>
     </td>
   </tr>

   <tr id="TMPL_VAR ID>">
     <td>2</td>
     <td>pip   </td>
     <td><input type="checkbox" name="field" f2>
     </td>
   </tr>

<form action="index.cgi" method="post">
    <input type="submit" name="Edown" value=" Download ">
    <input type="hidden" name="cmd" value="download">
</form>
[download]