Blower fan does not work in a/c mode, but if I switch it to heat the fan kicks on and starts blowing hot air.

What model is the furnace? It may be a bad relay, or circuit board, try switching the thermostat to the "on" fan position. Does this bring the fan on? If so you have a bad thermostat.

What model is the furnace? it may be a bad relay, or circut board, try switching the thermostat to the "on" fan position. Does this bring the fan on? if so you have a bad thermostat.

I disagree about the idea of "If you turn the fan switch to on". Some of the newer furnaces have a fan speed relay and a cooling speed relay on the PC board. Fan could still come on and the cooling speed relay is bad. Oh! The good old days when I could diagnose 95% of all HVAC problems without a volt/ohm meter.