How can I diagnose my fridge's evaporator fan?
If the fan is not working, you need to focus on that first. 


If you spin it manually, does it work? If so, the motor may just be old or clogged so starting friction is too high - try cleaning, then replace.
If you cannot spin it, check for obstruction. If none, replace.
Check voltage across the fan motor (with door switch open then closed) - if it doesn't turn on, then check electricals.


(It is a cheap and easy self repair)

Once you have got the fan working again, then check to see if problem is solved.