So is the computer powered up, but the screen is not turning on? Or is the computer itself staying in suspend?
My screen stays dark after exiting suspend because of a specific module I have. There's an easy script you can create and run to get around this issue though.
Create a new file and put it somewhere in your home folder. (screen.sh for example)
Open the file with a text editor and post this in it:
xrandr --output LVDS1 --auto
Now all you have to do is assign a keyboard shortcut to run this file. If your screen fails to wake up, this may help with that issue. For example, I have CTRL+S assigned to wake the screen if it stays black. This is what I have the CTRL+S shortcut run:
I'm using xfce, so I don't know right offhand where you assign keyboard shortcuts in gnome. But I'm sure it's somewhere that isn't too hard to find.