I have this 95 lexus sc300. engine 2JZGE. I am having trouble starting my car. The battery works fine. When i put the key in ignition non of those gauges sign comes on and my car won't even crank. There's not even clicking sound when i turn on my key. But when i open the door the door open sign in the dash comes on.Does anybody knows is this the starter problem or may be due to faulty ignition coil.

Check your fuses. Particularly the 120a one in the box under the hood.