I have a similar 2008 Samsung washer (WF206BNW/XAC) that I nearly trashed because it would not drain. It had a problem with the drain motor. I was able to fix the motor, but not before I had purchased a replacement drain pump motor. (which is in my cabinet should I need it in the future)
Before doing any work on your washer, disconnect the power cord and turn off the water. Be prepared to soak up water with towels or whatever, if you are dismantling the pump.
The problem with these pumps:
Water will get inside around the armature of the drain pump motor, but this part does not see the 120 volts which is limited to the stationary outer part of the motor. The motor will run with this water but eventually it builds up calcium and deposits that start to bind on the rotating part, which will cause it to draw more current. An overload on the outer part of the motor (coil) will open and protect the motor from burning out, but eventually that overload will fail and either burn or open circuit and no more power gets to your motor. The easiest thing to do is replace the motor which is readily available from a number of online stores. But if you are handy with your tools, you can dismantle the motor, scrape out the deposits from inside the plastic cylinder where the armature spins and remove any deposits on the armature. You should put a bit of high quality grease in the bearings before reassembly. I put too much grease in the first time and it dragged on the rotating parts and I had to disassemble it again to clean it out. You will need to check the overload device (heat sensor) that is tucked in the coil and stationary portion on the outer part of the motor.
However, if you replaced the motor and it still doesn't run, your problem is probably in the Control Panel, as was mine. Control panel circuit cards are not available anywhere!!! Check to see if you are getting any voltage to them motor terminals. If your have no voltage, continue reading:
The increased current causes the contacts to pit and corrode and they don't make proper contact anymore. Below see the little relay only 1 inch long, where I have exposed the contacts so that they can be cleaned
The trick is to get to these contacts and clean them up with a tiny bit of fine sandpaper. This relay in on the control circuit card, which must be removed from the washer to get at.
First remove the top of the washer by removing the screws at the top in the back.
push the top towards the back of the unit and lift off.
Remove the screws from the control panel and pull forward in order to remove the wires. Make a note where the wires are connected or take pictures before removing.
This is a picture of my control circuit card connection after I had cleaned the contacts and reassembled the wiring.
When you have removed the control panel, take a close look at the labelling under the relays (black boxes) and locate the drain pump relay. With an exacto knife gently cut around the top of the box and remove the top.
You have to gently remove the black plastic link that goes from the white actuator to the relay contacts with tweezers. When you do, it will look like the first picture in included above. cut a small strip of fine sandpaper and fold it in half lengthwise. It has to be small enough to fit inside the box between the two contact pads. Rub it up and down gently between the two contact pads while squeezing the pads together on the sandpaper using tweezers. do not oversand, one or two strokes is enough. Blow out any dirt.
Put the link back in position between the white actuator and the contact. Make sure that it moves properly by pushing gently on the actuator and the it closes the contacts.
I put a plastic box over all the relays and taped it in place so that dirt would not fall in the contacts after reassembly.
Reassemble the Control panel to the washer, but leave the top off during testing.