I'm getting the CE-34788-0 Error after having installed update 4.55

I've been away from my PS4 for over 4 months (studying abroad), and so I came home a couple of days ago and updated the console with 4.55. It updated fine, but was a bit slow. Oh, well, I thought. So I went to buy ME: Andromeda, put it in rest mode to finish the installation. Came back, woop-dee-doo, it's installed, so I play the game without a hitch. Played it again yesterday as well, without a single problem.

Well when I put it back in rest mode for the night, the console was doing a clicking sound, as if powering up, but remaining in rest mode. Now, today, I try to turn on the console but it's off (it turned itself off, from Rest). Turn it on, it boots in Safe Mode. It does the system storage check, but then says it can't turn on.

I get an error message that says I need to install the most recent update. So I do, and do the whole file formatting correctly, and it still doesn't work. I get the CE-34788-0 Error.

I made sure to get the right file (From this link: https://www.playstation.com/en-gb/get-help/ps4-system-software/) and it still doesn't work.

What do you guys think? Is this bricked or is there a fix? And if it is bricked, how do I transfer all my saves in my current situation?