Fridge not running

Looking at the picture and we know the white wire is common and the red wire would be run.I would be put it on the right side of the new relay on terminal 1 or 2 as we know from what I sent you both terminals are corrected so that would not matter. That being said the old relay is VERY reliable.You could be dealing with a failing compressor?

I am so appreciative of your willingness to assist. I will keep your advice close at hand.
2 questions if you will:
Will a failing cold control cause the intermittent start/stop of the compressor? My cold control showed open with ohmmeter whether off or on, which explains the no run that corrected with a new cold control.
If I pick the wrong side to attach the overload wire, will that result in a constantly energized compressor after startup, and then cause compressor failure?

Nice pics!
Not sure why you are trying the compressor relay as your issue appears to be the temp control.
BB is correct, that old relay is VERY reliable.
Round piece is the overload, part with the small coil is the start relay.
BB also mentioned the white is likely the common and the red is the power/run.
White went straight to to compressor terminal and then the red would go to the overload and the run side of the new relay (the one you posted) as being correct.

If the old relay still works, keep it and use that…JMO

jeff sr.