A few comments:

1. Don't print your HTML out in your Perl script. At the very least, use CGI's methods for creating HTML. Ideally, you'd use templates (a la HTML::Template, Template Toolkit, or Mason, to name a few).
2. Your SQL can very possibly break, if $company has naughty characters in it. I would use placeholders, if I were you. Something like:

   my $sql = <<__END_SQL__;
   SELECT DISTINCT name
     FROM master
    WHERE name LIKE ?
    ORDER BY name
   __END_SQL__
   
   # stuff here
   
   $sth->execute("%${company}%");
   
   # more stuff here
   [download]

3. You need to error-check your prepare() call as well as your execute() call. prepare() is where the SQL is checked for syntax. execute() is where it is checked against the database. A number of DBD drivers (such as Oracle) will dump out of prepare() if the tablename is wrong, or the like.

As for your actual problem, I would argue that you haven't through through what you want to do. I would build a list of $ag values within the while-loop. Then, outside the while-loop, I would check to see if you have any $ag values. If you don't, put your "Value not found" select. Otherwise, build the selects.

$sth->execute() || die $sth->errstr;
if ($sth->rows >= 0) {
  while ($pointer = $sth->fetchrow_hashref)
    {
    $ag = $pointer->{'name'};
    $ag_save = $ag;
    
    if($ag){
    print "<OPTION VALUE=$ag_save>$ag_save</OPTION>";
    }
    }
}
else {
    print "<OPTION>No Ag were found</OPTION>";
   }
[download]

If your query returns zero rows (i.e., if fetchrow_hashref() never returns a non-undef value), you'll never make it into your if test, and thus will never emit any <option> tags.

I'd guess that $ag is " " (or something like that -- a string of blanks). That non-empty value will evaluate to true, but will be - surprise - blank.

Something like

$ag =~ s/\s+//;
if ($ag)
.
.
.
[download]