95 Honda Civic wont start no click but it will push start and the lights and radio turn on

Check your battery voltage. Lights use very little amps and can still burn on a partially dead battery. Clean and tighten all your battery connections. If all that checks out check your clutch pedal switch. If it's bad this issue will also occur.

If you have good battery voltage you will need to check the switch wire signal. This is easily tested with a test lamp. The switch wire (smallest wire on the starter motor solenoid) is made live by holding the ignition switch in the crank position. You should have a voltage or signal when this is done if you have voltage then check the main supply lead from the battery . Common fault lies with poor or broken switch wire or faulty ignition switch not supplying the voltage.

I had the same problem. I shorted out the clutch pedal switch and it fired up. Replacement part is $40 at Advance.