Fan comes on but the air conditioner does not
There are a lot of possible reasons this could be happening, but here are some common ones:
1. Frozen coils
If too much moisture remains inside the indoor unit, it can freeze and form big blocks of ice around the refrigerant coils. Instead of cooling the air, the refrigerant just keeps making more ice.
There are several common reasons for icing, especially if the unit has been running for a long period of time:
1a. Icing due to clogged drain
If the condensate drain out of the unit is clogged, the backed up water causes elevated moisture levels in the air inside the unit which form ice on the coil. As more water sitting in the drain pan evaporates, the ice gets thicker.
Find the condensate drain from the indoor unit and check it. How to do this will vary depending on your unit.
1b. Icing due to poor airflow
This is most commonly seen on units with very dirty air filters. The airflow through the filter is restricted, meaning that not enough air is flowing through the coils. As above, the moisture condensed on the coils freezes. It can also happen if the return vents are blocked by items in the house.
2. Failing capacitor
Inside the outdoor unit of your air conditioner, there is a large capacitor that is used for starting the unit. If this capacitor fails, the outdoor unit won't run and the refrigerant won't circulate. Make sure the thermostat is calling for AC (turn it really low) and go outside and see if the fan and compressor are running. If they are not, listen closely to see if you hear a faint humming noise. If you hear the hum, you need a capacitor.
3. Low refrigerant
You probably need to get an HVAC professional to check this one - they have special tools to measure the refrigerant flow through the system.