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A couple of comments on your code:

You should use placeholders for values where possible for many reasons, including security, problems with quoting etc. That is you should change

    my $stmt = "SELECT * FROM $table WHERE $key_col = '$key_val'";
    my $sth = $dbhandle->prepare( $stmt );
    $sth->execute();
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into

    my $stmt = "SELECT * FROM $table WHERE $key_col = ?";
    my $sth = $dbhandle->prepare( $stmt );
    $sth->execute($key_val);
[download]

You should errorcheck your database stuff. Add a || die $DBI::errstr to all your DBI->connect, $dbh->prepare and $sth->execute.

You only need two row, so only get those. That is change:

    my $ref = $sth->fetchall_arrayref();
    $sth->finish();
    return map { $_->[$name_col] => $_->[$val_col] } @$ref;
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into

    my $ref = $sth->fetchall_hashref([$name_col,$val_col]);
    $sth->finish();
    return map {@$_} @$ref;
[download]

print "Content-Type: text/html\n\n"; is wrong. The HTTP standard says it should be \r\n\r\n. However most browsers dont care ;)
Dont use a & in a sub call without needing it. It overrides any prototype you may add at a later time to make perl check the number/type of params to get_hash.
Dont overgeneralize. If you only use get_hash for this specific purpose, then fill in the tablename/colname and select only the two rows you need instead of *.

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