When you state " The temps seem to stay consistent in LP mode" does that mean that LP works correctly......food section 35*F & freezer 4*F (give or take)?
When you plugged fridge into an extension cord....assume you mean plugged the fridge AC power cord into an extension vs the outlet in TC?
You can run simple test....unplug AC heater element from control board and plug it directly into an extension cord then check temps next day. (bypasses control board---checks heater element capability and IF control board is issue).
Also you can check AC heater element amp draw....should be 2.5A at 110V AC
And the resistance should be 61.3 ohms at ambient temp (range of 58-64 ohms)
Check AC heater element connections/terminals...loose, worn, corroded will affect how well they preform
AND...check draft of outside compartment. Any obstruction....fallen down insulation etc. causing blockage will affect ability to cool as outside temps change