[hatzie]

Basic Principles of Refrigeration
Liquids absorb heat when changed from liquid to gas

Gases give off heat when changed from gas to liquid.

For an air conditioning system to operate with economy, the refrigerant must be used repeatedly. For this reason, all air conditioners use the same cycle of compression, condensation, expansion, and evaporation in a closed circuit. The same refrigerant is used to move the heat from one area, to cool this area, and to expel this heat in another area.

The refrigerant comes into the compressor as a low-pressure gas, it is compressed and then moves out of the compressor as a high-pressure gas.
The gas then flows to the condenser. Here the gas condenses to a liquid, and gives off its heat to the outside air.
The liquid then moves to the expansion valve under high pressure. This valve restricts the flow of the fluid, and lowers its pressure as it leaves the expansion valve.
The low-pressure liquid then moves to the evaporator, where heat from the inside air is absorbed and changes it from a liquid to a gas.
As a hot low-pressure gas, the refrigerant moves to the compressor where the entire cycle is repeated.
Note that the four-part cycle is divided at the center into a high side and a low side This refers to the pressures of the refrigerant in each side of the system

TANSTAAFL... If the belt is off the compressor then there's no cooling at all.
The compressor has to compress the refrigerant or there's no refrigerant state change to liquid at the condenser and back to gas at the evaporator.
No state change = no cooling. End of story.

I assume the evaporator froze up and you expected the block of ice to thaw quickly when you pulled the belt. Nope. Ain't gonna happen. Once it's frozen solid there's no airflow through the evaporator. It could take several hours to thaw even on a good hot day.
Don't believe me? Set a 6" x 3" x 12" solid block of ice in the shade. You may be shocked how long it takes to thaw even on a relatively hot day. The evaporator box is mildly insulated. It could take a very long time to thaw out.

You are not getting 22°F out of the vents. 22°C (71°F) I can believe... 35°F vent temps are possible but too low as the evaporator will be below the frost temp of 32°F or 0°C. You want vent temps in the 40-45°F range with outdoor ambient of around 85°F... without driving the high side pressure into the stratosphere when the outdoor ambient temps climb into the 100°F area.

A freezing evaporator is either a low refrigerant charge or restricted airflow. Intake to the blower? Mice or leaves or...