I'm using version 3.4.2 and my deleted posts are still rendering....

How can I fix it?

Thanks!

swap to the default theme and see if they are still there.

If you actually delete a post, it is removed from the database and can't be seen unless the page is cached somewhere. Clear your browser cache.

I cleared the cache and that didn't delete them.

How do I switch to the default theme?

go to the wordpress dashboard->Appearances->themes and locate the default theme, then click activate.

I switched to the default theme, cleared all cache history, and those posts are still rendering. The problem is that even if I redid the posts, it would just appear as a duplicate. There's a get_post() in functions.php, but no delete_post()...

How can I get to the database and delete the posts?

What version of WP and PHP?

are you saying that if you go to the Wordpress Dashboard, then to 'Posts' -> 'Edit' - that if you select a post, wordpress won't delete it?

if so, I think you have a wordpress problem.
First off, you sould backup your database and the contents of wp-contents.
Next switch to the default theme.
Third, disable all pluging and see if you can delete a post if that doesn't work, you could try wp-dbmanager and try to repair your database.