If you hear a fan running on high- it's most likely because a sensor is damaged. The default condition when a heat sensor malfunctions is to run the fan at maximum in order to prevent further damage to heat sensitive components like the CPU. Examining the board under a magnifying glass might find or point out corrosion or burned components. You may need to examine both sides of the board.
So the problem is probably not the fan, but a sensor. Sometimes you have to run AHT 2 or 3 times in a row to get useful results... especially if it's an intermittent, or, overheating problem (if the unit isn't hot then the problem won't occur). If it tosses out an error the complete text of the error usually indicates which sensor has failed. So maybe you only need to replace a sensor.
At this point, with the machine not working, you have little to lose and much to gain... you just have to decide how to spend your money. In decreasing order of cost:
A liquid spill is not a covered claim under Apple care - try asking for a depot repair (that's the best price Apple repair).
You might try a local shop that is Apple Certified and see what they wold charge.
If you have good reading comprehension skills you could try to do the logic board replacement
yourself. Study the guide - before you begin, especially directions/cautions about disconnecting cables etc. Most problems and damage come from someone tearing a connector off the board because they didn't unlock it, or, pulled in the wrong direction or way.
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