I would accomplish this with a state machine of sorts. Write your loop without delays so that on each pass, it checks the sensor. If there is movement, it resets a variable, say lastMoved, to the current millis() . If the current mills() - lastMoved is greater than 120000 (2 min), it turns on the led.
Please enter a valid email to subscribe
We need to confirm your email address.
To complete the subscription, please click the link in the
email we just sent you.
Thank you for subscribing!
via Egeo 16