When temperature got warmer today, the air conditioner would not come on. The pilot light was off on the furnace. I tried to light it a number of times, but the flame would go out when I released the igniter button. Does pilot light on furnace have to be lit for air conditioner to come on?

No

Can you tell us what is your AC doing. Does anything run does anything click. Are there any sounds.

The only thing that may be common with the pilot light is if your pilot safety is tied in with your 24v limits. So if any limits open up it kills 24v to the system and your pilot safety not letting the pilot burn or nothing work. If your blower will run when you turn the fan switch on at the thermostat that rules that out.