one has nothing to do with it as it only increases RPM under loading conditions (AC etc). Warm the engine up, unplug the AAC while it's idling. If nothing happens either the base idle is set too high or the solenoid is dead. Set the idle to 650 when it's unplugged and then plug is back in. It should go to about 750 instantly, if not the AAC is probably dead. You can test it like any solenoid with 12 volts to see if it clicks.
Other things to check: TPS setting, Coolant Temp sensor for in spec. All connectors are corrosion-free.