Not sure where to post this so I guess it may be moved.

The washing machine is just out of warranty and though it lights up when turned on nothing happens.

Could it be the switch or could it be the belt ?

Make and model would help the experts; some models need the supply power off to reset a fault code trip and this will be in the fault diagnosis section of the manual. Sometimes only imbalanced load or blocked discharge pump filter after last cycle.
Also without a belt, you should still hear the water fill, you could hand turn the drum, if there is a resistance the belt is attached.

The door interlock is a good place to look as the machine will not start if the door lock does not set on. Just done one on my machine which is about 18 months old.

DWD