If the SerialNumber is unique then just add a form to each row with that as a hidden value

if($c->param("searchTerm")) {
  while ($row = $q->fetchrow_hashref) {
    my $bgc = ($i % 2 == 0) ? 'background:#DDD;' : '';
    $results .= qq!<tr style="height:30px;border-bottom:1px;$bgc">
<td>$row->{SerialNumber}</td>
<td>$row->{AssetTag}</td>
<td>$row->{AssetType}</td>
<td>$row->{Branch}</td>
<td>$row->{Status}</td>
<td>$row->{Comments}</td>
<td>
  <form method="post" action="modify.pl">
    <input type="hidden" name="SerialNumber" value="$row->{SerialNumbe
+r}">
    <input type="submit" name="modify" value="Modify" style="font-size
+:15px"/>
  </form>
</td></tr>!;
    $i++;
  }
}
[download]