I am assuming by "ice box" you mean the fresh food side.

I would not worry about the fresh food side right now, it is the freezer that is important as all cooling originates here.

When you say the fan is running, do you mean the evaporator/freezer fan?
It must run for the unit tto cool properly.

Is the compressor cycling or on all the time?
If it is cycling then there is probably a thermostat problem.

Remove the cover in the freezer so you can inspect the evaporator coils.

If they are heavily frosted/iced over then you have a defrost problem.

If there is no frost or just frost in one area then it is probably a sealed system problem.
This test must be done after the unit has run continuously for a couple hours.
If you do it shortly after a defrost cycle then there of course will be no frost.

Here is a good link for basic fridge troubleshooting/repair info.
http://www.applianceaid.com/frig.html