Hello and welcome.
Well, the most common cause for a security light and the car to not start is the Passlock cylinder.
This is a common failure on many GM cars.
The fact that it starts after 10-15 minutes leads me to believe this is your problem.
The waiting is basicaly a relearn of the theft password, which tells me the BCM is functioning and able to relearn the password XXXXX Passlock sensor gives it.
Not to say i have not had a few BCM's cause this over the years, but 98% of the time it is the Passlock sensor.
Actiually, since it is so common, when we have a problem car and can't descide which one is bad, we ALWAYS do the passlock sensor first. Almost always takes care of problem.
Hope this was helpful,