PHP conditional script issue

You have a lot of PHP tag spam, e.g.:

?><?php

This is bad, confusing, makes your code difficult to read, and a waste of your time to type. It’s the difficulty reading your code that has lead to your problem, including the lack of indentation. These are important, and any good editor will do them for you effortlessly.

If we remove the PHP tag spam, and indent correctly, we get this:

<?php
{
    if ( is_front_page() ) {
        get_template_part('home-page-content');
    } else if ( is_page('archives') ) {
        get_template_part('archives');
    } else
        get_template_part('secondary-page-content');
}
?>

Firstly, there is a set of braces surrounding the whole thing, serving no purpose ( except maybe to confuse ). Remove these, giving us:

<?php
if ( is_front_page() ) {
    get_template_part('home-page-content');
} else if ( is_page('archives') ) {
    get_template_part('archives');
} else
    get_template_part('secondary-page-content');
?>

Finally, we have coding standards, so lets put braces around the final else statement:

<?php
if ( is_front_page() ) {
    get_template_part('home-page-content');
} else if ( is_page('archives') ) {
    get_template_part('archives');
} else {
    get_template_part('secondary-page-content');
}
?>

We can go further, those are a lot of calls to get_template_part, what if we only called that function once?

<?php
$template="secondary-page-content";
if ( is_front_page() ) {
    $template="home-page-content";
} else if ( is_page('archives') ) {
    $template="archives";
}
get_template_part( $template );
?>

However, all of this implies that you’ve overloaded one template with too much responsibility. I suggest you look at the template hierarchy, that way we can use the frontpage.php template to remove half of that if statement.