If the Samsung Washer has no error codes but when you go to start it only clicks, you may have a motor capacitor issue, wiring problem, or a possible bad control board that is not communicating properly.
You can test the motor capacitor to be sure it is working. If the capacitor goes out, the washer motor will not start or run.
When the washer did run for 1/4 of a cycle, did the washer make any strange sounds?
What did the washer do the moment it died out in the middle of the wash cycle?
No flashing buttons or beeping sounds?
Did the washer still have full power when it stopped mid cycle?