Air conditioning removes condensation from the air. That condensation is turned into water on the coils of the AC , drips onto the pan and exits at the drawn at the back of the AC. Condensation occurs when the humidity in the warm air "condenses" on a cold object. Condensation does not occur on warmer objects.
You see this on windows in the winter ..... when warm inside air condenses on cold windows. Also take a cold glass of ice tea, can of beer whatever and put it on a table and you see droplets of condensation forming on the cold surface. OTOH, have you ever seem water droplets form on the outside of a hot cup of coffee ? Heat increases the air's ability to hold more water. Cold decreases air's ability to hold water, so air near the cold surface will cause that moisture in the moisture to 'fall out" of the air into the cold surface
In a PC, the only time I have seen this happen is when using:
1. Dry Ice cooling
2. LN2 Cooling
3. Water cooling using "below ambient" water source.
In your PC, if the PC is ON, then the components will be hotter than the air in the room, therefore, no condensation.....if the PC is off, then the components will be in the same temperature as in the room, therefore condensation can not occur.
In fact one of the ways to remove moisture from an electronic object is to put it in the refrigerator. I have resurrected a dozen or so phones from death after they were dropped in or they got thrown in a pool, simply by putting in a fridge overnight.
The only way your AC could be a culprit here is if it's uninstalled improperly and mounted above your PC. Condensation can occur on the cold coils / heat exchanger and when it drips onto the pan, if the unit is installed tilted forward rather than back, it would drip inside the house.