If you start it and never rev it up, it does not have a skip. Once you rev it up and let it come back to an idle, it starts skipping and shuts off. When you try to restart it, it sounds like the timing belt has broken(no compression). You can eventually get it started, but it skips. As you let it idle, the skip goes away and it runs smooth.
I have replaced Cyl head, lifters, PCM, fuel pump, removed CAT.

Any help would be appreciated.