"My heater doesn't come on when I start my car"

HVAC is BCM controlled, so could be programming glitch or an ignition switch not sending an ON signal for that system.

If you're talking about the blower motor, yes, it's likely a BCM ow ignition switch problem. But if you're talking about the heat, as in hot water circulating to the heater, you probably just have a level of coolant that's too low for it to circulate properly when the engine's cold, or a failing thermostat.

The Avalon can be on for 20 minutes and the heat still does not come on, the fan works. I have to shut the car off and turn it back on for the heat to come out of the vents. The heat the defrosters work all day long after that.

Might be a stubborn thermostat. But the Limited also has a climate control system that can be problematic with age, and yours is thirteen years old. Find the unit and spray electrical contact cleaner into it. If that doesn't work, see a mechanic, it might have gone out.

Still sounds like a signal issue.