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.
This is a good idea for sure. Just make sure that you don't use int as your datatype or you'll get some weird stuff going on. Sometimes when I write code quickly I'll do something dumb like that then when it doesn't work I'll scratch my head for a while and then eventually find the problem and feel like an idiot