Why does my PS4 slim skip safe mode and will not boot?

My Playstation 4 slim will not enter safe mode (pressing the power button until the second beep). Whenever I do, it goes into a white light and my monitor says no input. After a few seconds of hanging on, it starts again, but with an error message CE 34335-8. The same error occurs when I normally power it on, except it shows the Playstation logo before it goes to the error screen.

I’ve tried to power cycle the system and even try to boot into safe mode with no hard drive. What could the problem be and could it be possible to fix without sending it into Sony?

Quick edit: I bought the system from someone on Ebay. He only mentioned it would not read his hard drive, which was partially true. I tried a few of my tested HDDs to confirm. What wasn’t included in his description was the safe mode trouble. I’d love to reinstall the system software, but it seems like a fun challenge.