Toyota Repair: 2005 Avalon XLS, 5000 Miles, Transmission Problem?, service bulletins, factory warranty

Question
Believe I have two problems - not sure. When traveling with the transmission lever in Drive position & applying brakes slowing the car to approx 3-4 mph, then step on gas pedal, there is a 1-2 second delay or slippage before the transmission takes hold.  If I come to a complete stop, then step on the gas pedal, the transmission shifts correctly. Other problem - On three different occasions when turning on the key to start the car, the engine raced up to full throttle. Foot was only on brake pedal not on gas.Had to turn key off and then car restarted properly.  Your thoughts?  

Answer
I have not heard of these concerns and there are no service bulletins from toyota regarding these issues.
Since it is still covered under the factory warranty I would recommend that you have the toyota dealer check for any possible causes.
Most of the time any engine or transmission malfunction will turn on the check engine light on the dash on, is this the case?