Starting problem 2003 Pontiac Grand Am

I have a 2003 Pontiac Grand Am. We have intermittant problems starting the car in the morning. We had only one set of keys when we bought the car and purchase additional keys that were not genuine Pontiac keys i.e. just from a hardware store. When we try to start the car and turn the key to the start position all the interior and exterior lights go out except the service enigine soon light. We have had the batery and connections checked by a mechanic and have had a new starter installed. Our mechanic seems to thisnk this is a security problem with the keys so we had the codes reset and still have the problem. Once the car is started and driven it starts fine untill the next morning. Anybody have any ideas? Thank you for your help.

My initial guess would have nothing to do with the keys, but rather with the ignition switch itself. Do you know if your mechanic spent any time checking that out?