Kenmore fridge runs but doesn't cool (model # 596.71813101)

[TCO]

Kenmore fridge runs but doesn't cool either chamber.  Model # 596.71813101 S/N: 0103164073

 

Only thing I have tried is power reset (no help).

 

Please advise as to troubleshooting advice or if you think I should call a repair tech or replace the unit.

[TCO]

Just saw the flow chart.  I will look at it (not near now) and try to figure out if compressor and condenser fan (not sure how to tell which is which...I do hear something running!) are running and if dog hair an issue.

[TCO]

I went over to the condo and looked at the machine.  Think the condenser fan is running and the grate not dirty.  Felt air coming out back grate and it didn't seem too dirty.  That left me at "is the compressor running", which I don't know how to tell.  I mean there was some noise...but that might just be the fan. 

 

The air inside the chambers was moving from the little vents at top back...does that mean the compressor was also running?

 

Am I at the red oval of buy new fridge?