All the CGI is going to get from the browser is whether the checkbox is checked or not, you need to keep track of the data to display yourself. Assuming the arrays you are displaying are available in the submit.cgi as well, you could change your checkbox to something like:

<input type="checkbox" name="check" value="$_">
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Then in submit.cgi you can check which boxes were checked:

my $cgi = new CGI;
foreach($cgi->param('check')) {
    print "<tr><td>$a[$_]</td><td>$b[$_]</td>....</tr>\n";
}
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