Usually you can't move extruder before hotend is heated; this is a safety feature as extruding to unheated hotend might break things.

For Z-axis, you could try:
- connect only one motor at a time, just to see if they work individually
- rotate only other connector
- check the amps the stepper drivers are outputting. I don't know what kind of board that printer has so it's either measuring voltages with multimeter or mucking around in the firmware.
- check the steps/mm in firmware or in the printer menu. If it's Marlin, it's Control->Motion->ZSteps/mm