So I've had this issue since I got my PS4 at launch. Basically, if I turn on my PS4 before I turn on my TV, nothing will display once the TV is turned on. Likewise, if I turn my TV off while the PS4 is running and displaying, it won't display anything when I turn the TV back on. I'll try unplugging the HDMI cable and plugging it back in, but still nothing. I always end up having to turn the PS4 off (but not unsafely like by pulling the cord, just holding the PS button and scrolling down 5 times to "Turn Off PS4"). Anybody else ever have this issue and/or know how to fix it?

Nope.

Here my PS4 turn one my HDTV... and if I'm already watching something I just hit PS on controller and it will change to PS4 display.

In any case every time I hit the PS button on controller will display the PS4 display on HDTV.

PS. You can try desativate this feature the options: http://manuals.playstation.net/document/en/ps4/settings/devicelink.html

My TV doesn't output sound when I turn the PS4 on before I turn on the TV. In my case, it helps when I switch to another channel (HDMI 2 or TV or something) and then back to the PS4.

I had a somewhat similar situation with my PS3. Not as severe though.

Never did solve the problem unfortunately.. ended up getting a new TV at some point and the problem never carried over.

Can't even do that. If I turn on the PS4 while I'm on HDMI 1 and then switch over to the PS4 on HDMI 2, it won't display anything.

I guess it is imcompatiblity of the  HDMI Device Link with old HDTVs.

Maybe he can disable it.

Sounds like an issue with the HDMI control/power feature on your TV.  In your TV setting trying turning it off. 

Try some tests with.

[System] > [Enable HDMI Device Link]

This, wow, you beat me too it.  This is what I meant but cound't remember the exact name.  

I do *occasionally* have a slightly similar issue when using a PC monitor instead of a TV, but only when HDCP is turned off, in that i get sound but no video, if i dont switch inputs to hdmi before turning on the ps4, this happens about one every 15 boots.

A quick and easy solution for me is to just unplug the hdmi cable and plug it back in again, on the rare occasion it actually occurs.

Do you have HDCP turned on or off? also do you have HDMI control turned on or off, for the TV/PS4, some tvs will have this issue on 360/ps3/ps4/xbo over hdmi if its enabled but not fully supported by the tv.