How to test if user is denied access when her role has no "access content"
I recommend saving out your permissions using Features and then loading your custom feature in your test. By doing that, you can test out your configuration settings.

If you really just want to turn programmatically create a user that does not have the 'access content' permission, try this before you create your $web_user:

user_role_revoke_permissions(1, array('access content'));


This will revoke the 'access content' permission for anonymous users (role 1). See http://api.drupal.org/api/drupal/modules%21user%21user.module/function/user_role_revoke_permissions/7 for more help.