Thanks for the detailed post.
(First you can try running Origin as Admin... see if it lets it install, if it does skip the rest of the top part of course)
Do a System Restore to the day before you even started trying this game. I want to start as fresh as we can.
Go to: C:\Program Files (x86)\Origin Games
Delete or Rename the 'Plants vs Zombies Garden Warfare" folder
Open Origin try downloading + installing again... If it installs and gets to the point where you have the Origin no open error... stop. Don't uninstall / reinstall the game anymore.
---------------- For Origin error in game
Is Origin installed on the HD / Partition as the game? If not reinstall Origin to that HD/partition. (uninstalling or reinstalling Origin does not uninstall the games themselves, might need remapped if it's a non-default location though)
Is this your first origin game and just made the account recently? Maybe you have to activate your account via email or something?
Go to the PVZ.Main_Win64_Retail.exe, properties, compatibilty, "run as admin"
Run Origin shortcut as admn.
Do a Clean Boot:
