Yes the radiator is either empty or low. Fluid should be above the fins inside the radiator all the way to the top. As for the battery, you can have power and lights will come one, but when turning your key to the start position, the starter pulls alot of power, and if the connection is loose or weak, its possible under hard load to crank, that the connection can cause it to not maintain that load. All you have to do is grab the positive terminal at the battery and twist it alittle to see if it moves one way or the other, the do the same thing for the negative side. Its the not turning over or no clicking sounds that has me wondering about the starting side of things. You can also set the park brake and put your transmission in neutral and see if it turns over. This will test the park/neutral safety switch on the tranmission. If that doesnt work, put the vehicle back in park.