I acquired a site that was ranking on page two for competitive query. Moved it over to custom version of WP and 90 days later had #1 ranking. WP was not a hindrance.
I love that old book, "Don't Make Me Think". The techniques may have changed some but it's still true that if you site isn't easy to navigate and find things people won't stay.
Excellent read. Site navigation architecture should be idiot proof - for both your human and SE users.
Regarding valid html - I have a past client who's site was a markup nightmare (over 300 errors and 40 warnings), mostly because of bad design. His designer clung to the theory that markup was unimportant. To prove otherwise, I started with a basic WP theme and outranked the other site in a few weeks with just few low quality links. Draw your own conclusions.