This can vary with custom themes, but is outlined here: http://codex.wordpress.org/Creating_a_Static_Front_Page
Please check out:
http://codex.wordpress.org/Moving_WordPress
It should have everything you need. Basically you could move your WP site to a subdomain or a directory like: blog.yoursite.com or yoursite.com/blog
Then just link your static site to your WordPress.
503 errors are not permission errors, that is absolutely incorrect.
503 Service Unavailable
The server is currently unavailable (because it is overloaded or down for maintenance). Generally, this is a temporary state.
http://en.wikipedia.org/wiki/List_of_HTTP_status_codes
