Ok so if that light is coming on then we can rule out the power supply.
If nothing is coming on then its normally the thermostat that causes this but it doesnt normally effect the light in the fridge.
Have you removed the bulb to see if its blown?
As to the thermostat you need to remove the light cover and you will see the screw holding the light fitting on.
Remove this and then pull out from the back and the front of the thermostat housing will pull off from there.
Then you can see the thermostat from there.
Make sure its unplugged and then you can remove it.
You will see 3 tags on there marked 3,4 and 6.
You need a test meter and check between 3 and 4 and see if theres contonuity. If there isnt then the thermostat is faulty and will need to be replaced.
Check that if you can and see what you find from there.