Hello cassiecar77.
Welcome to the HP Forums! I understand your Deskjet 3520 power light keeps blinking. Does this happen when the printer is in idle or when printing a document?
Are you receiving any error message on the printer?
Make sure this printer is plugged into a direct wall, not a surge protector.
Try Resetting the Printer. Leave the power cord out of the printer for at least 60 seconds.
Looking forward to hearing from you.