I don't blame you.
Here's what Sony says about this.
If none of that works, you are staring down a tech support call and possibly sending it to Sony.
Make sure you got a FAT32/exFAT usb hdd and back up your HDD before you send it in-- Just in case. I've heard that sometimes they send you a new PS4 and in that case, I'd rather have the peace of mind knowing that I can put my stuff back on my own in case they botch transferring my stuff. I wish you luck. Worst case scenario is you'll need to get a new ps4, which will stink really bad. (That'll only happen if it's too expensive to fix.)
Also in case you're curious,
here's where I originally read about this problem. I also have a older model PS4, so I might be staring down this eventually, but mine's been a trooper.
Oh and btw, that reminds me. *backs up her PS4 hdd while she's thinking about it* Good luck with this; this sounds like it really stinks. Also with the beeps thing; I was checking a video and it's 1 when you first hit power button, another about 5 seconds later if you keep your finger on the button, so you should be able to get away with using a timer instead before you let go. (One that works for hearing impaired folks). Just start the timer when you first put your finger on the button. if it works, you'll see something about "connect a controller"; that gets it into safe mode btw. ^^ Where you can run some diagnostics; it really looks like the only problem for a deaf person is the beeps, since the safe mode screen is well..on your screen. ^^