The car has powerful new battery (1 week old). I drove the car and after 4 hours, the car will not start, not even click when you try to start the car? All the lights are ok and they are not dim. What could be the problem?
Editing my answer
It had happened to me a couple of time and common symptoms that I found are
Loose Battery Connection
Somehow the battery terminals got loose, tighten it and it will solve the problem. It happened to me before.
In my latest case, even tighting the termainsl didn't work. I had to get a jump start. Even with jump start the car was reluctant to start and then it started only we started the other car. The increased amperage solved the problem. Could it be the battery, No. I had new battery installed 2 weeks ago.
This is the likely cause if all other lights work but your car does not click. This is the switch you turn in the key or it could be part of it that is connected to that mechanism in the steering wheel. To troubleshoot this, turn on all your lights, try to start the car. If the light dim considerably, your ignition switch is OK. In my case, when I opened the ignition switch, I saw a bandage around the Ignition Switch that propted me, may be this is the problem but I am not sure yet.
It could be that the starter is bad. It is good idea to check with a mechanic and see what could be the likely cause. A mechanic knows which cars comes with which problems. In some cars it is the starter that usually fails and that way you dont have to guess elsewhere.
As another answer says, it could be just the solenoid that does not wants to engage.
Again from another answer, the ground may be not good enough
Bad Starter Connection
So this seemed to be my problem in the first place :) The car will not start, not even click but all lights are ok. Put a stick and touch the wire on the starter and wow the car starts! I wonder what really is wrong but it is just touching of that wire that makes the car from no-start to start.
Hope it helps
Since you've only driven the car 4 hours with a new battery, the most likely thing would probably been a loose wire on the battery. Check the big wires and the small ones both.
One other possibility that hasn't been mentioned is that a safety switch on the brake pedal or gear shift level may not be switched. Try wiggling the gear shift lever and brakes. If that doesn't help, check out the switches.