BIOS screen doesn't load

When I am afk for a longer time, the systems goes on standby. The screen is black.
Generally I just press the power button and I am on the normal Windows screen from where I enter Windows.
However today when I pressed the power button, nothing happened and the screen stayed black (when I set the screen on then off it displays "No signal".

I shut down the power and restart.
The fan works, the HD seems to do something (there are no beeps but then I think there never were before) but the BIOS screen never appears.
Tried ctrl+alt+del, ctrl+alt+esc, del and f2 after power up but nothing happened.
I did all this about 10 times but the result is always the same - black screen and no BIOS.

My system is :
Processor : I7 975
MB : Asus P6T WS Professional
Graphics : GeForce GTX 295

What should I do ?

Thanks for the advice.
However before I started attacking with a screwdriver, I tried one last time to press the power button.
This time the BIOS loaded followed by W10 without problem so that I am in my system normally again.

But that also means that I should have the possibility to access tools which could tell me what went wrong and most importantly what to do to avoid that it repeats.
Can you advice me what to do and what to check to find out what the problem was ?

As I wrote, I didn't press the power button only twice!

I did it at least a DOZEN of times with no BIOS loading and only the black screen.
But it is true, as I also wrote, when the computer is idle (I am afk) for a certain time it goes to "sleep" or "hibernation" (whatever the difference between these 2 terms is).
That means that the screen goes black but the system stays under power (the power light is on).

Normally the system "wakes" when I press the power button and gets me to the W10 loading screen.
It was only today when the system seemed to "sleep" as usual and I pressed the power button as usual that nothing happened and the screen stayed black.
Then I did the cycle shut off/start up about a dozen of times ALWAYS with the same result - black screen and no BIOS screen .

Then, after the advice of Compumind, before starting to spend an hour with a screwdriver I tried one last time to start up and everything happened normally. BIOS screen came then W10 loaded as usual.
So it seems to me that this problem has something to do with the "sleep" or "hibernation" when idle but I have no idea where or how to look it up.

Well after 2 days it happened again.
This time it was not during the system's "sleep".
Yesterday evening I shut down the system properly but this morning I have the same problem - black screen, BIOS screen doesn't load.

I am ready to try Compumind suggestion but I don't understand it well.
"Start up with integrated graphics" - I wasn't aware there were integrated graphics on my MB.
But if there are, I'll have to connect the screen to something (now it is connected to the GTX), right ?
How do I connect the screen to the "integrated graphics" ?