Code for activating a led after 2 minutes and will blink after 30 seconds interval
Use a commonly available USB power pack re-charging from mains and powering the Arduino.  Use a light source directly powered by main and optically couple that to an Arduino.  There are plenty of examples on the web where an Arduino is used to detect light.  Once triggered, write some additional code to blink the led.  Since you are not doing anything other than timing, you can use the delay Arduino library to time events.