iMac grey screen at start up

I have a genius bar appt tomorrow but was wondering if anyone might know what is happening. My mac just stopped one day. Clicking sound and than black screen. I shut it down and turned it on. There was a grey screen with green vertical stripes and then went to all grey. Nothing else. My son in law did everything he knew, we did a safe boot, ran diagnostics (Which said no issues were found) but it still is just a grey screen. I can't back up anything to remove things before bringing it in so I was curious if anyone had a similar problem? I did buy apple care and it doesn't run out unto October 2015 but I am hesitant to leave the computer there since I am unable to turn it on to back up and remove items. Thanks so much!

You have Apple Care and that's a good thing. And if you haven't kept up with your backups and that's a bad thing. You can ask the genius if they can extract your data for you, but there's a chance they won't be able to. I had to take my iMac to the genius bar because my hard drive had failed but luckily I had a recent backup. The genius will tell you whether they can backup your data or not.