Im sorry but what do you mean specifically by output? I measured the adapter directly and got 12.44V.
Also, when i replaced this new adapter, the fan now works and its spinning but its like not exactly reacting to the temperature anymore? like the readings are all still wild when i connect the power adapter even if i try to pinch the LM35 its still going crazy jumping from 3 to 30 degrees celsius, with the fan running at a normal rate.