Problems staring when cold on 2006 Lincoln Zephyr

i started experincing this in nov the battery was low dealership replaced it. Problem continued they replaced fuel pum , plugs did work on manifold very costley repair. Car still wont start when cold. I have also noticed it runs and starts better when over half tank of gas. Have tried adding dry gas, letting car sit for a while before driving. intermittently it runs very rough.

1 answer
Yikes! is there any trouble code available?