Premiere Pro CC turns off one of the monitors before crashing--HELP?!

I just installed Adobe Premiere Pro CC on my desktop, which has Intel Core i7, 3.20 GHz, 16 GB of RAM, and double video card on it. This is an Alienware Aurora ALX from 2011 with Windows 7 Home Premium. I've imported all the videos I need and once I start editing, about three minutes into working, it turns off one of the monitors. I have two monitors hooked up and one of them loses signal--it literally says the monitor has "no signal," which can't be true because I never touched the computer. So I tried unplugging and plugging back in, still no difference. And now when I reopen Premier Pro CC, not only does one of the two monitors go black, but the computer freezes. It's done this five times now and the only way to get the machine going is to turn it off manually by pressing the power button. I can't get past using the program for more than five minutes max before this crash occurs.

Is this a video card issue? A different hardware problem? Is it the program? What can I do to overcome this issue? I have multiple projects I've got to work on and if I knew I'd run into this problem, I probably would not have purchased the program... I'd be grateful for help/solution from someone!