Either Blog On Homepage OR Static Page With Everything Missing

I have been trying to figure this out for hours.
I want to have my blog on a different page from my homepage.
I have figured out how to do that: set the homepage to static and select a different page to house the blog. That moves the blog just fine–however, it totally destroys the homepage.

Why does static a homepage lose all of its other functionality? If I have a static homepage all of my widgets disappear along with the jumbo headline and the sizing of the background image.

Why is this an either/or? Why can’t I keep my homepage as is and just move the blog?

Please help.