Here are your parts
Parts for LG LRFD25850TT / ATICLGA Refrigerator - AppliancePartsPros.com

Below is a link to a manual.
You will have to join the site and be logged in to be able to download it.
http://appliancejunk.com...wnloads;sa=view;down=335

When you say "Compressor "seems" to be running fine" do you mean that it is cycling on/off as it usually does?
If it is then the problem is with the electronics/sensors that control the compressor.

If the compressor is on all the time except when it goes through a defrost cycle then it is a different problem re: the unit knows that it is too warm but for some reason the compressor cannot get the temperature low enough.

Also not sure what the coils looked fine means.
The below only apply if the compressor is on all the time.
If they were heavily iced/frosted over to the point that the evaporator fan could not pull air through them then it is a defrost problem. It does not sound like this is the case.

If there is just frost in one area usually where the freon enters the coils then it is a sealed system problem and it will be an expensive repair.
Below is a link to this type of problem, see the 3 example pictures part way down the page.
http://www.applianceaid.com/ref...ator-not-cold-enough.php

It important that the test be done after the compressor has run for at least an hour. If you do it during or shortly after a defrost cycle you could end up with the wrong diagnosis.

If it looks like a sealed system problem check your warranty as sometimes the sealed system has a longer warrant.