GE TBX18JA refrigerator is not cooling. Is there anything we need to check before we end up throwing this one out and having to buy a new one?

Check defrost timer and defrost heater. Find defrost timer. Turn shaft of defrost timer with flat blade screwdriver until refrigerator turns off. Wait approximately 30 minutes. Refrigerator should come back on. If it does not replace defrost timer.
If refrigerator comes back on after 30 minutes, check defrost heater.

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Turn refrigerator off for 1 day with doors open. That will allow any ice build up on evaporator coils to melt. If refrigerator then functions properly, that would indicate a defective defrost timer or a defective defrost heater. You could then begin determining which one is defective.

The first thing you check is under the unit by unplugging it and removing the rear cover where you can see the condenser coils. You will need to also remove the front kick plate. Wash out coils with a light spray from a water hose then vacuum up water with wet vac. Use Windex or another cleaner on fan blades and it also helps to remove greasy dirt on coils. If it was extremely dirty that may have been your only problem. While you are down there see if the defrost timer is there and if so plug in unit and rotate timer (do not run unit for more than a minute with rear cover off as many units require cover on to route air through coils.) until it clicks and compressor turns off. Wait 15-30 minutes and while waiting see if freezer is defrosting. The freezer fan will be off and steam should rise out of freezer and you will hear it as defrost heater heats up. If unit comes back on without any defrosting then the heater and/or the defrost terminator are bad. Unplug and replace rear cover, then remove cover to freezer. You will most likely have to defrost freezer to get the cover off. Inside you will find a defrost heater element and a round t-stat wired in series with it and attached to the side of the coils. Test heater with an ohm meter and if it reads open replace both heater and terminator. Many times you will see heater burned in two, especially on side-by-sides which have a glass tube with an element inside. Another thing that can be bad is the freezer fan, so be sure to check it too. Check it out and get back to us.