I have a gas water heater, the pilot lights but the burner won't fire up.?

If the pilot lights and stays lit it is NOT the thrmocouple. If the thermocouple is bad it shuts off all gas including the pilot.

Are you certain that you have turned the gas valve from pilot to on? Next turn the temp dial, , , do you here the thermostat clicking on and off? If so then as last resort tap on the gas valve with a screwdriver handle, not a hammer.

If that doesnt work then you need to replace the entire control valve. Thats a medium diffuculty DIY job. The control valve will run you about $60 from a plumbing supply store.

If your tank is relatively new and has a sealed burn chamber then you have to call a plumber.

Some times the thermocoupler is funny. Have a plumber come out an check it. I had the same problem last winter. We had someone come out for about 50 bucks and they adjusted it. No problems since. Maybe there isn't any gas getting to the burner.

you must direct the pilot lite to hit the thermocouplings end so it sends a signal to the main switch to turn on the gas.

the pilot lite heats up the end of the wire and therefor it signals the main that the pilot is doing its job.

just physically, with a long-nose pliers, direct the flame to the thermo wire end

You probably are not holding the button in long enough for the flame to catch. You have to hold the button in for at least 60 full seconds and maybe longer.