iMac monitor goes dark; 2nd monitor ok

Greetings. I am a new member to this forum, though I have read many posts over the years.

I have a dual monitor setup on my iMac (2009) running Snow Leopard (10.6.8). The iMac monitor (21") had been working great, but now it goes to a black screen when I boot up. I am able to access it briefly (for about a second) by lightly pressing the power button on the back. The iMac monitor flashes on briefly when I do this and I'm able to quickly click on user. I used this same method to open Settings and drag it over to the 2nd monitor to change the display setting to Mirror mode, so I'd have access to the dock on the 2nd monitor (Dell 2007WFP).

I have tried the following so far:
checked cables
booted in Safe Mode
reset SMC
reset PRAM (I believe this was reset, but I don't know for sure because I couldn't see anything on the monitors.)

Other information:
2.66 GHz Intel Core 2 Duo
8 GB 1067 MHz DDR3
NVIDIA GeForce 9400

Thank you in advance for any help with this problem!

It could be anything from a loose connection inside to an intermittent or defective backlight in the monitor. It has to be something in the monitor itself since you're receiving normal video on the Dell. For the time being until you can repair it don't shut down. Put the system to sleep. Learn how to take apart your iMac at www.ifixit.com.

Thank you so much for the reply. I will check out that website.