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Replacement parts for General Electric TFX27PPBABB Refrigerator | AppliancePartsPros.com

lights come on inside. fan inside runs. fan in back next to compressor runs.
compressor sounds and feels like it is running.....no cold.
Remove the cover in the freezer section and check the evaporator coils.
Check to see if there is any frost on them at all.
If there is just a little or it is splotchy then you may have a low freon condition.
If there is no cooling at all and you are sure the compressor is running either the compressor is toast or you are out of freon.
Any of the above are fairly expensive repairs as you require a pro to fix it.
If it is just low or out of freon there is no use re-filling it unless the leak is found.
Here is a good link
http://www.applianceaid.com/refrigerator.html
Check out #20, the example pictures at the bottom of this page. Note the first one does not work.

I let it run one day for a while and it seemed to just quit running ie fans and compressor after about an hour without getting cold
Could be it just went into a defrost cycle. It should restart in about half an hour. You can force it out of defrost by turning the defrost timer cam Item 257 in Section 4.

If you confirm that it is not cooling and the compressor is running and you decide it is too expensive to repair, you may want to try giving the compressor a couple good smacks with a 2 by 4. Do not hit it too hard you do not want to dent it, also do not hit it on the start relay. Perhaps it is frozen and this may knock it loose. After all at this point you have nothing to loose. Try it with the unit running and if that does not work with the unit unplugged.
This is a last ditch longshot at getting it going.