no water comes out from the brewer head

If the machine has power (heats, lights come on) but the pump doesn't make a sound when either the coffee button is pressed or the steam knob is turned, then yes it's possible the pump is completely dead. This is very rare though so I would make sure to check all the wiring and ensure the pump is getting power.

Pump does make sound, but nothing comes out. Steam wand works fine.

Thermal fuse which on the white wire may be blowed, use ohm meter to check,