My GE freezer stopped cooling. I turned it off,

Try disconnecting the power at its source, then reconnecting it.

The unit needs two fans running and good airflow, one fan outside cools the condensor coil and the other inside the unit blowing across the evaporator. The compressor must start up. The defrost timer stops everything and switches on a heating element to defrost the evaporator for several minutes. Please verify these conditions.

Put the old board back in. See what it does, from your post, sounds like it was working correctly.

Obviously, the compressor is not running. Confirm the presence of power to the compressor itself. If it is getting power and unit does not run, you have an open motor winding OR if you have a start capacitor the latter could be defective. Let's hope that you have the capacitor because they go bad and are a lot cheaper to replace than the compressor!

This sounds like the temperature monitor is alarming because the temperature has not cooled down enough yet in your freezer. turn the monitor off until the freezer reaches proper temperature then you can turn it back on.

Is this a frost free freezer? If it is, and the compressor and refrigerant is good, the problem probally lies with the defrost timer. What the defrost timer does, at regular intervals, typically every 12 hours, shuts down the compressor and powers up a defrost coil to melt any frost that has built up on the cooling coils inside the freezer. It probally the small square box that you mentioned. Some have a hole where you can turn the cam to the timer and that should switch the power from the defrost coil to the compressor.

Hope this helps.

My freezer was purchased in February, 2004. It is a self defrosting freezer but ice has started forming along the bottom shelf and back wall. Also, after cleaning the freezer the other day it has stopped clycing. The freezer will stop running only if I turn it down to the #1 setting and then it will not come back on. If I turn it up to a higher setting the compressor will not stop running. It ran for over 24 hours and would not cycle unless I turned it off or set it at the #1 setting. When I unplugged it and pulled it away from the wall, there was a green water spot the size of a dinner plate underneath the freezer. Help!! Very Unhappy this freezer is only 6 years old. S in Phila.

freezers have a range of ambient temperature uses
most are plus 10c to 35c if using some units in garages etc. they just dont work...too cold for the poor things...

Probably a defective defrost timer. Try to find the timer. It is usually underneat in the back. When you find it turn the knob slowly click by click. (You may need a screwdriver or knife) turn just until the compressor stops. Let it stay in defrost for about 1/2 hour. turn the knob until the compressor starts let it cool down several hours. Then do it again. If this solves the problem replace the timer. While you are waiting to do this Defrost it at least twice a day by turning the knob.

Service:
http://mrappliance2.reachlocal.net/land/
http://www.sears.com/sr/service_order/so_productinfo.jsp
DIY repear and diagnosic help:
http://www.acmehowto.com/howto/appliance/freezer/freezer.php
http://www.repairclinic.com/0047_3.asp
http://www.fridgedoctor.com/