You do not say what brand you have, If a Norcold the thermister is about a $15 deal. I carry a spare. It is clipped to the fins. Remove it and place in a glass of ICE WATER. It should read 30-32 K ohms @ 32 degrees.
You say it is the same on both elec and Lp, that points to a thermister. To test the cooling unit, locate the 2 wires that go to the elec heaters. You may have 2 elec heaters. (4 wires) They will be plugged into the control board. Remove from the board and hard wire them to 120vac. Let it sit overnight. In the morning the frig part should be around 25 degrees on the middle shelf. If not the cooling unit is bad.
On a '11 model frig you probably should not need to "burp" it, but if everything else checks out, it does not cost anything to "burp" it. When you turn it upside down, let sit over night and when you rotate it back 90 degrees have the boiler side down for a few hours and then back upright. Let sit 6-8 hours upright before turning it back on. You can re-install it, just don't turn it on.
Since your frig is in a slide the 2 fans on the back must be working.
When looking into the back if you see any yellow power residue or smell ammonia, you need a cooling unit and do NOT use it on LP.
You can download a service manual here:
You can buy a cooling unit here:
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