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Sony doesn't guarantee that every drive that physically fits in the PS4, and meets the basic specifications, will actually work with the console. Seagate had to do some unusual things in the design of that drive to put enough data on each platter to provide 2TB of capacity in the 9.5mm form factor. I expect that the PS4 is not the only device designed a couple of years ago that would have compatibility issues with it.
I came to the conclusiion if your PS4 came with the HGST hard drive, it does not work with samsung hard drive 1TB or 2TB.
After asking around on the net, others have had similar problems to me. It turns out a correlation has been found between what the PS4 original hard drive came with. Mine came with a HGST. Others have come with Samusng Spinpoints. If yours came with a HGST, it appears you will not have luck with the Spinpoint 2TB or 1TB. If yours came with the Samsung, it should work fine with the Spinpoint hard drives.
Thanks fox_1047. I guess the M9T 2TB hard drive (and the M8T 1TB) is just not compatible with PS4. I reported this issue to Sony's phone support with the hope that if enough people complain, they may resolve the problem. Others should follow suit. I hope HGST comes out with a 9.5mm 2TB that's compatible with the PS4.
After further research and testing, I found one additional method to get the hard drive to boot successfully. Just hold down the power button 6-6.5 seconds after the beep just before safe mode is triggered. Holding the button down allows the hard drive to fully spinup before the HDMI handshaking takes place. Note, if you hold the button too long (7.5 seconds to be exact), you will get into safe mode and have to try again.
Another slightly modified method is to push the power button and release after 2 seconds after it beeps. Then hold the power button for 4-5 seconds and release. This is easier than the previous method because you have more time before you get into safe mode (because safe mode requires the button to be held continuously for 7.5 seconds).