Monitor turns on then shuts off in seconds.

tried two diff. monitors , both do same thing. ran virus scan. reported trojan, recommended starting in sfe mode. followed prompt and tried safe mode. screen went blank.tried botting from disc, monitor now will not stay on. cant get started on fixing virus problem with no monitor. dell computer. not sure if monitor problem is coincondience or is related to virus. when i pull cable out it stays on to advise "no signal" so i know it is not monitor. graphics card??? could a virus damage this? dont know where to start. by the way i am sending mail on different computer, not to worry for viruses. thanks