Your laptop is likely in hibernate, which is why the power button is blinking. Try holding the power button down for 10 seconds and see if the blinking stops. Then, if you have an easily removable battery, pull that out and hold the power button for 10 seconds again. Then plug the battery in and try charging it.
If this doesn't work (or you can't remove the battery) you may need a new cable, or for a PC tech to remove your bottom panel/palmrest to get to the battery for a hard reset or replacement. A good one should have a multi-meter and be able to test your current power cable as well.