After installing, and playing, Battleborn, my PS4 was no longer able to download anything. I tried everything else first; logging out/in, removing disc, restarting, power cycling, deleting extra space (even though I had plenty), rebuilding database, and deleting the Battleborn save file. Removing Battleborn completely from the console was the only fix.
I had 30 gigs available, and was trying to download an update for a game that is 3 gigs on disc, and then I tried to download a new game that was 10 gigs in size (to make sure it wasn’t just the update with the issue).
With Battleborn installed gave the following error:
Error code: CE-37704-1
NAT Type: Type 2
System Software: 3.50
Message: Cannot download. To download the content, you must delete unnecessary content from system storage.
After deletion of Battleborn, I was able to download with no issue.