May be the monitor cable, but most of the CRT monitors you can't easily replace,(looks like a TV), LCD flat screen monitors, yes. My thoughts are that it's the power supply. Have you ever cleaned the inside of the computer out, plus the fan, and internals on the power supply, with a can of compressed air for computers? (Long sentence, huh? lol!) When dust, hair,(animal usually), carpet deodorizer, etc. builds up inside a computer, it clogs the fans,(case fan/s, processor fan, power supply fan), and also contains static, the number one 'killer' of computer parts. I'd say 90% of the computers I receive to work on,( I do 'er part-time), have burned up power supply's. Why? Either they're cheap units,(Which computer manufacturers put in because it drops the selling cost. Some of the newer ones have decent psu's,(power supply unit), which have gone to solid capacitors, and use voltage regulators, better rectifiers, etc.), or the owner/user doesn't clean their computer out regularly. Burn's 'em up. Usually one of the electrolytic capacitor starts to fail, dropping one of the voltage rails amps down below tolerance. Computer starts acting weird, then one day, Nada!
research +da brain=the answer