PS4 Plants vs zombies

The splitscreen is accessed on the tv in the back yard.

If the second controller cannot turn on the PS4, it probably needs to sync with the console.  Just use a charging cable to plug the controller into the system and then push and hold the PS button until it lights up.

Both controllers need to sync with the system.

This article might help:
https://manuals.playstation.net/document/en/ps4/basic/usecontroller.html

... and more articles troubleshooting splitscreen:
https://answers.ea.com/t5/forums/searchpage/tab/message?advanced=false&allow_punctuation=false&filter=location&location=forum-board%3Apvz-garden-warfare-2-general-discussion&q=splitscreen

Good luck.

I suspect splash has nailed it.  However, here are two things people often get wrong when using split screen:

1)  Make sure the PS4 is set to be the "home PS4."  A quick google search will show you how.  Otherwise, the second player will only be able to play as "guest."

2)  Make sure both players are logged in to their PS accounts.  If the second player is not logged in, they will still be able to play as "guest," but they won't accrue any progress.