iMac screen goes dark

I am having a problem with my iMac computer screen going dark unexpectedly. This can happen at any time, during any program.  It can usually be brought back for awhile by pressing the main on/off button on the back of the computer, pausing for a second or two then pressing the button a second time and it will turn on. It then might stay on for  an hour or more but more likely once the problem starts it keeps happening, often staying on for only a second then going dark again. Any program in use at the time continues in the darkness, e.g. if there is audio happening, like on a YouTube video, it will continue in the darkness. Keyboard commands still work. The mouse still works too but it can only be directed during the one second that the screen is visible before it goes dark again. If I then leave for a couple of hours then come back it will usually work again for a while, sometimes even for a few days, then the problem starts again. Re-starting doesn’t seem to have an effect.

Whenever I wake the computer there is a telltale sign that the problem will happen or not: If the screen brightens in two steps, i.e. 1/2 brightness then full brightness, then the problem will not be appearing for a few hours, maybe days. If the screen reaches full brightness immediately then I can look forward to a problematic session.

I am using OS X El Capitan version 10.11.6, on an iMac (21.5-inch, late 2009)

Processor   3.06 GHz Intel Core 2 Duo

Memory   4GB 1067 MHz DDR3

Graphics   NVIDIA GeForce 9400 256MB

Serial Number W8****5PC

[Personal Information Edited by Moderator]