Hi. What model Vaio? Search for what the different flash patterns signify via models technical manual. Can probably find the document at Vaio support site. Will the device turn on without RAM installed? Look that up to see. Same w CPU. If one or the other is malfunctioning to the point it's not being picked up... possible could cause the issue if the component(s) required for power-on.
Did you go back to the machine several minutes later to try again after it has cooled? ie, does it overheat? That might stop it from turning on.
If it's not starting on AC power with battery removed, and it's not anything else, could be a bad charging port on the machines motherboard. Have you ever had issues where from Windows the battery's status switches from charging, only to fix by wiggling the power connector? I've had that one with 3 laptops... Too fragile I guess, and people yanking the cord out or jamming it in a bit too indelicately, or having it too close to a wall, w pressure applied, etc.. damages it over time. The part to replace is like .50 cents but it require soldering the sensitive equipment. They charge like 100 - 200 to do the work at repair shop..
All I could think of though. Hope it helped!