Sounds like the dispaly, cable or cable connection.
Rule out display issues: If your Mac won't turn on - Apple Support
In or out of warranty you can get a free over the counter 'Apple Service Diagnostics' test and ask specifically for the VST (Video Systems Test)
Genius reservation http://www.apple.com/retail/geniusbar/
on-line https://getsupport.apple.com/GetproductgroupList.action
check warranty https://checkcoverage.apple.com/