After I killed the Warrior his dead body is between the green button and me and I cannot press the green button to call the Moon Shot to finish him off. I can see the green button but there isn't any dialog. How can I end the game and kill Jack?
As BenBrocka pointed out, quit your game (ie exit out of the menu), and load your game again. You'll continue the game from the same area as the fast travel before the Warrior fight.
Don't join a friend's game or anything, otherwise you have to do the whole Hero's Path fight against Loaders again.
All credits go to BenBrocka
Also, additional tips from the gameFaqs forums:
Happened to me, I jumped in the lava to die, and then fast traveled to pass. ran back through and his body was in the right spot and I could hit the button. It DID glitch out hilariously though and fake Jacks kept appearing and attacking, and running through the cutscene, like when lilith said "no rest for the wicked" and one ran right in front of the screen, I almost died laughing
No need to quit, die or fast travel. I had this same issue but was persistent until I found where I could click the button. I had his head on top of the console and was unable to click the button even if I stepped inside of his head. I could see the button covered in green "click me" highlight, but I didn't get the prompt to press "e". I crouched down on the right hand side of the console, facing the button, and was able to click the button at a very specific angle.
IF your quest objectives are "Call the moonshot" and "Kill Jack" and "End This", then QUIT the game without exitting the map, then use CONTINUE from the main menu. The Warrior will be dead BUT it will be repositioned to its correct location, and you will just have to click the button, at which point you'll get all the Warrior loot etc. and the quest will continue normally.