1996 Pontiac Bonneville Starting problem!

Electrical problem
1996 Pontiac Bonneville V6 Front Wheel Drive Automatic 100000 miles

I have a 96 Pont. Bonneville about about 4 months ago I replaced the engine and everything was running great, no problems. Here recently about once a week it seems when I go to start the car nothing happens, the dash lights stay on and there is nothing not even a sound, if I wait a few minutes so far it has started and I have been able to make it home. I had the battery checked(good), the terminals were clean but I cleaned them anyways, I even changed the starter (I had an extra one off my old engine) but the problem keeps happening. I am thinking it is now in the ignition switch(?) But am only guessing. Could you please help I am afraid my my wife and daughter could get standed somewhere.
Thank You Larry