I would look at two things:
First, if you are using HTML:Template, your TMPL_VAR tags don't look right... they should have a "name" as well:
<TMPL_VAR name="fname">
Second, it looks like you are doing your assignments the hard way. If you return an AoH (Array of Hashes) from your call to DBI, you can assign that entire array to a loop within your template. For instance:

my $p = Page->new();
# now we get the info from the database and pass it to the template
# in this case, the template needs a reference to an array of hashes
# in order to handle the TMPL_LOOP properly.  Which is exactly what
# dbselect returns.  hard to believe :-)

$newst->param(news => $p->dbselect($sql,1));


sub dbselect{
    my Page $self = shift;
    my $sql = shift if @_;
    my $hash = shift if @_;

    my $db = $self->db();

    my $h = $db->prepare($sql) or $self->errorpage("DB problem in sele
+ct prepare: " . $db->errstr());
    $h->execute() or $self->errorpage("DB problem in select execute: "
+ . $db->errstr());

    my $arrayref;
    if ($hash){
        $arrayref = $h->fetchall_arrayref({});
    } else {
        $arrayref = $h->fetchall_arrayref();
    }
    return $arrayref;
}
[download]

I'll break down what just happened there. I'm using an object called Page (I use it for web pages in general), it has a method called dbselect that will query the database for me (the connection is set up elsewhere). $newst is an HTML::Template that I have genereated, so I call the param method of $newst with the output from dbselect assigned to the TMPL_LOOP news. It then fills in my news page with rows of news. Some day I'll update it to limit the number of stories, but I'm basically boring so I don't have that much news to display :-)
Note the call to fetchall_arrayref({}) within dbselect. Read up on the documentation for DBI, in this format it returns AoH.

The template that uses this looks like this:

<table border=0 width='98%' cellspacing=3 cellpadding=3>
    <TMPL_LOOP NAME="news">
        <tr><td>
            <table width='100%' border=1 cellspacing=1 cellpadding=0>
                <tr>
                    <th align='left'><TMPL_VAR NAME='summary'></th>
                    <th align='right'><TMPL_VAR NAME='pubdate'></th>
                </tr>
                <tr>
                    <td align='left' colspan=255><i>By: <TMPL_VAR NAME
+='realname'></i></td>
                </tr>
                <tr>
                    <td align='left' colspan=255><TMPL_VAR NAME='conte
+nt'></td>
                </tr>
            </table>
        </td></tr>
    </TMPL_LOOP>
</table>
[download]

So you see, by using the AoH with a TMPL_LOOP, I was able to loop through everything with almost no code. Very easy once you understand it.