Ice in fridge, on back wall, high up, even with stat turned to minimum

well yes and no , defrosting it will temporally make it work , but main problem is there isn't proper air flow over evaporator coils id clean them with soap and water while defrosting out unit , if low airflow is allowed to continue then refrigerant gas will build to high press and escape and render unit a total replacement

There is a defrost timer on the unit. It is supposed to come on and melt the ice that forms on the coils in the evaporator. IF you get a lot of ice built up or something is wrong with the timer, it wont melt the ice or it wont come back on to cool the unit.

you have a defrost problem,bad defrost heater,thermostat,sensor or computer board,your gonna need a meter to see what's bad,go here
http://www.searspartsdirect.com/partsdirect/part-model/GE-Parts/Refrigerator-Parts/Model-GSH25JSTASS/0432/0165000/G0604755/00003?blt=06&prst=0&shdMod=GSH25JSTASSthis is the parts that are behind the back inside freezer wall,look at 230,240 and 243 and on the outside back of the machine is the computer board part number wr55x10942,hopefully it won't be the board,shut down the machine and remove the back inside wall of the freezer,then go in the back and remove the cover of the mother board,you'll see a metal panel it's behind it,look at the bottom of the board,you'll see a gray plug with three connectors that it's plugged onto,you'll need a jumper wire with alligator clips on the ends,clip it on j9 and j11,this is the middle and the metal to the right in the gray plug,this will turn on the heater in the freezer,,plug the machine back in,if the heater comes on you have a bad board and change out the sensor if it has the black ring on it,no matter what you have to change the sensor if it has black on it,if it doesn't come on then check the thermostat and the heater,unplug the heater and check it for continuity,also look at the heater,if it looks black inside the glass change it out and change out the t-stat,if the heater is good check the t-stat,part number 240 in the picture,also you can cut the two wires going to the t-stat,connect them so you bypass the t-stat and jump out the board again,if the heater comes on the t-stat is bad and this is the most common part that goes,also if there's a white plastic ring around the top of the t-stat and it's popped up on one side it's bad,water got inside of it,froze up and pops the top off.here's a picture of the board and how to jump it out
http://www.flickr.com/photos/zenzoidman/4482598198/sizes/o/in/photostream/

j9 and j11.and here's another picture that might help you http://fixitnow.com/wp/2008/11/04/how-to-test-the-defrost-system-in-a-ge-arctica-or-profile-refrigerator/
you can leave the heater on to help you melt out the ice and with a hair dryer melt out all the ice on the coil,also if you need time to get the parts and stuff if you remove the back inside wall of the freezer and melt out all the ice on the coil your fridge will run for 10 to 12 days and then it will freeze up again but your food will stay good and then hopefully you can have what you need to fix it.hope this helps and good luck.

If you have a fridge or fridge freezer and the fridge is not getting cold it will be one of the following problems:

1, The fridge thermostat is faulty and not cutting in at the required temperature. Fridge stats are not easy to test, so the best way is to bypass the stat to see if the compressor starts. To bypass the stat first unplug the appliance and remove the stat housing from inside the fridge compartment, once you have removed the housing you will see the stat inside. Some stats have 2 terminals some have 3, whatever yours has you will need to connect the compressor wire ( Black) to the live wire (Red or White). When you have bypassed the stat plug the appliance back in and switch on, if the fridge starts up and runs ok you will need to purchase a new stat.

Types of thermostats:

There are various types of stats fitted to fridges and fridge freezers, the most common being the VT9 (pictured below) this stat will replace most larder fridge stats and most conventional fridge freezer stats. If your fridge has an ice box inside then you will need a VC1 type stat which has different temperature ratings. If you have an older Zanussi or Electrolux fridge freezer with one compressor and the stat is in the fridge then you will need a Reverse Action stat, as these type of appliances have a solenoid valve fitted into the pipework near the compressor and the stat operates the solenoid.

If you are replacing your old stat with a VT9 and your old stat only has 2 terminals then connect the new VT9 using the terminals marked 4 and 6 only. When fitting any new thermostat take great care not to kink the capilary tube as doing this will render it useless.

2, If you have tried bypassing the stat, and the compressor did not start then you have probably got a faulty compressor. To test for this is quite simple just listen carefully to your fridge and if the compressor is at fault you will hear a faint hum followed by a click, you will need to be patient as once it has clicked it could be 10 mins before you will hear the hum again. The reason you hear a hum is because the compressor is jammed and the hum is the motor trying to turn, the click that follows is the thermal overload tripping. If you have these symptoms it will not be worth repairing due to parts and labour costs.

3, If your fridge has lots of snowy ice on the backplate this is a sign that either the door is not shutting properly and letting in warm air thus creating snow, or it could be that you have lost some gas from the system and the compressor is working over time trying to get the temperature down. BE ADVISED it is rarely worth getting your system regased unless a leak can be located, as the gas will only leak out again and you will have the same problem in 1 or 2 months.

Frostfree fridge not cold

If you have a frostfree fridge freezer and the freezer is ok but the fridge is warm then your appliance is not self defrosting correctly, and if you could see inside the back wall it would be full of ice, this ice is blocking the airflow to the fridge compartment and therefore your fridge is warm. A quick fix for this problem is to completely defrost the appliance to do this you will need to move your frozens to another freezer then switch off your frostfree at the plug and leave off for 48 hours with the doors open and a large towel in the freezer to catch the water. After 48 hours plug it back in and let it run for 4 hours and you should find it will be working fine again, but you may find you will have to do this procedure every 6 months or so.

You have a defrost problem going on. Either the defrost timer, the defrost t-stat or the defrost heater. Remove the back freezer wall and you will see the evaporator coils. This is where the heater and t-stat are located. One of these is more than likely the problem.

Defrost cycle has problems. Could be defrost timer, heat element, or defrost stat. temporary solution, if you can see ice accumulated inside the fridge on the back wall, desconnect or turn it off, until this ice it's gone, can be use for couple days, until service could be done on it.

Does your model have independent thermostats for the fridge & freezer???

If not, could be that you will need to change the Thermostat.
These are not expensive - around £10 if you buy on the Internet.
Easy to fit yourself...just turn off the power, remove the power plug from the wall, then unscrew the 'stat unit from inside near the top of the fridge (some are attached to the interior light) and remove the screw holding the thermostat tube to the rear wall.
Often the thermostat gets a small hole somewhere in the long tube, which then lets all the gas escape, making the stat useless.
You can see these small holes in the pipe if you use a magnifying eyeglass, like the kind Jewellers use.

Sounds like the start of a defrost problem, open your freezer and see if the back wall has any frost on it. if so your evap coil is in-packed with ice and it won't be long till you start to lose cooling in the freezer also. If you don't have ice on the back wall check the evap fan motor to hear if it's running ( you should hear it when u open the freezer door or feel the air movement.) note: if the evap fan motor is not running that may also cause frost build up on the back wall of the freezer. If the fan is not running remove the back wall and check the fan wires for 120 volts ac.if you have power replace the motor. Also with the back wall removed you can check the defrost t-stat and defrost element you should read a closed circuit on the heater and with the evap coil frozen you will also read a closed circuit on the t-stat to. If the defrost element or t-stat check bad replace that part, if they check good replace the defrost timer. you can hit the coil with a hair dryer to thaw it out till you get the part you need, that will buy you about 3 days. Good luck hope this helps you

Is the back of the freezer section iced up?
If so you could have a defrost problem. All the cooling components are in the freezer section there is a damper controlled by a dial in the refrigerator that opens and closes.
If the damper is closed it will not allow air into refrigerator section. It is seperate from the Thermostat.
If the damer is opened to much you can start freezing food in the refrigerator section.
If there is ice on the back wall of the freezer section. It is not defrosting. There are 3 parts in the defrost process. The thermination stat, the heater, and the defrost timer or it's a timer on the electronic board behind the metal plate on the back of the refrigerator.
Good Luck

what is the stat set to ? A common problem with bottle coolers that work the same way, is people turn the stat to high ( very cold). This then drops the evaporator temperature so low it freezes up, in turn this stops the airflow and the ice build up worsens until you get the result you have, a warm fridge due to no airflow at all. It could be short of gas as this can cause it. A faulty defrost heater / timer can also cause it if its fitted as can a faulty fan that stops spinning. Due to the age of the unit I would try turning the stat back to 3/4 and see how that goes. it will get cold but will be more gradual, but hopefully shouldn't freeze up.