I guess some context is good. For me I'm talking a Mac Mini mid 2014 running High Sierra. I put it to sleep sometimes via the power button, and my "moment" holding down the button is probably a bit over a second. What happens usually is that the screen first goes dark, but when I was stuck in screensaver mode the screensaver continued. Typically it takes 10 seconds or so after I've held down then released the power button before the little "on" light on the front of the Mac Mini starts its slow blink to show it is asleep. In this case - stuck in screensaver - the 10 second wait did result in the screen finally going dark and the "on" light going to the slow blink. Waking up the computer had the screen back.
I do find the following at some other mac forum, and though they were talking older OS's like Mavericks and Yosemite, I do find this to work this way for my computer/OS version. Well, the 1-2+ second is what I normally do, so I just now only tested the 3-5+ second method to get the dialog box.
- 1-2+ second hold = sleep
- 3-5+ second hold = dialog
- 8-12+ second hold = force shut down
The resulting dialog box when I held down the power button 3+ seconds looked like this:
I'm guessing in stuck screensaver mode a 3-5+ second hold-down of the power button might not do any good because you probably wouldn't see this alert. And if you hit Enter, though it didn't show up here in my Grab - the Shut Down key was highlighted (dark blue), which means it would go for shutting down.
Unless when you tried the sleep method you possibly held the power key down a tiny spec of time less than a second, it sounds like the "hard sleep" method won't do it for you. But I'm putting all this out here in case it helps someone else who stumbles upon it (and who perhaps doesn't have the second computer/remote desktop option).
For me I'm going to remember your method because I have an older Mac Pro that is networked and if this ever happens again and my "hard sleep" method doesn't work, I'll give the remote connection a try. I also wonder what plugging in via USB and powering up a printer or a powered desktop external hard drive would do? That does wake up a sleeping computer...
(I do the "hard sleep" method quite a bit because my two macs are actually both accessed by one mouse/keyboard/monitor and I switch between them. When I am using both and want to put one to sleep, the menu method doesn't work because switching to the other computer wakes up the one I just put to sleep. So I have to use the power button method on the mac I want to put to sleep while I'm actually accessing the other mac.)