From looking on a couple of (what I think are) websites where you'd be getting your parts to clarify what I'm about to say; The GPU that system is going to require is already going to put you over budget. Nevermind the entire rest of the system. It would do well for you to tone back your expectations of the build. Also, if you could give a couple of websites that you would buy from that would be useful.
As stated, $400 does not even by the graphics card for 4k, let alone the entire rest of the computer.
$400 will be a stretch to even get you an entry-level gaming pc to play at low-medium settings at 1080p