What is the brand/ model of your PC. Google "(Brand/model) blinking green light on the back" or go to the manufacturer's website support area. Like HP.com or Dell.com - whoever made it.
Some of them have a breaker switch that needs to be reset if it is tripped. Different brands do it different ways. I had one where you unplugged the power cord and then held the power button down for a minute.
Also, on the back near where the cord goes, many older ones have a switch (not the switch that turns on the PC) that is for the power supply. You may need to toggle that switch.
It is most likely a simple fix.
Have you tried a different outlet? Try it in the one that it was originally plugged into. Yes, sometimes, it really will make a difference.