DevTools: Re-land r169860 with UI fixed (empty boxes and missing Styles toolbar buttons)

TBR=pfeldman

Review URL: https://codereview.chromium.org/208653013

git-svn-id: svn://svn.chromium.org/blink/trunk@169937 bbb929c8-8fbe-4397-9dbb-9b2b20218538