this is a very popular problem caused by different issues, one of the following solutions might work for you
lets start with the basics
basically the first thing you might want to do is changing the graphics card and if that doesn't work , you can try the following methods
1. have you wondered if the problem is with the screen and not the cables?
2. also consider that it might be the iMac's display mode that's not configured properly.
3. the problem might lie with the SMC , and if thats the case you, you should read more about it here. its a topic on how to reset your mac's smc http://www.macissues.com/2014/04/11/when-and-how-to-reset-your-macs-smc/
4. if all those options fail, you might have to replace the motherboard itself and if that also fails..... you will have to take it back to the store and use your warranty