The freezer and the refrigerator temperature fluctuate from 30 to 55 in the refrigerator. The freezer freezes and then melts. Do you have suggestions?
Here are your parts
http://www.appliancepartspros.com/partsearch/modelsearch.aspx?model=gs6shaxkq01
When the temperature rises are the fans also off.
This would indicate that it is in a defrost cycle.
Could be that the defrost thermostat (Item 35 in Section 11) is not opening after the ice/frost has melted off the coils and is adding too much heat into the freezer.
Could be that the main control thermostat (Item 9 in Section 10) has gone intermittent. If the fans are running and the compressor is not and is not rying to then that is where I would start. Just turn the thermostat up/down a bit or give is a tap. If the compressor fires up I would replace the thermostat.
Also check that the condenser/compressor fan is running and that the condenser coils under the unit are clean.
Check that the evaporator fan in the freezer is running whenever the condenser fan is running.
Here is a good link with basic fridge repair info.
http://www.applianceaid.com/frig.html