First I would try the DB query with hardcoded values - ignore the form inputs and make a query that you know will work and see what happens. When you have that working add some print statements - first to the $db_query that you construct from the form parameters to make sure it is what you think it is (examine it closely), and then the $total to make sure you are getting something back. And so on...

    $db_query = "SELECT ST.sno_name,HT.homolog_name FROM sno_Table ST,
+Homolog_Table HT,sno_Homologs SH,Organism O 
WHERE ST.sno_id=SH.sno_id AND SH.homolog_id=HT.homolog_id AND HT.org_i
+d=O.org_id and (ST.family=$family) and
O.organism='$TB'";
    print "db_query: $db_query<br>"; # add this
    my $sth = $dbh->prepare($db_query);
    $sth->execute();
    my $total = $sth->rows;
    print "total rows: $total<br>"; # add this
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Also, fix your td tags:

<td>$sno_name</d>

should be:

<td>$sno_name</td>
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