The green screen is fairly logical, as Amiga's won't start without ChipRAM

The 4000 doesn't need a battery to work, mine's never had one (I got the guy I bought it off to remove it).

I'm a bit stumped really - if it were mine I'd swap the Warp Engine off for a standard 3640 CPU card and see if that helped.

http://wonkity.com/~wblock/a4000hard/deadprob.html

This page details some possible causes - most likely is a looses CPU card - I've had problems with this on mine even after re-seating it.