Teresa,
I have just had the same problem with my AEG - I removed the pump using a pair of large pliers to squeeze the wire clips together and then slide them away from the pump. Watch out for the dirty water – put an old towel or rag under the pump or use a wet and dry vacuum. The black plastic mounding that fixes to the grey housing to the left, when viewed from the front, has two lugs that need levering up to allow the pump to be removed. The lugs are at the outside edges. I used an alan key to lever up from the bottom.
When I had removed the pump I used an old length of mains cable with a plug on one end and a couple of spade connectors on the other, plugged into the pump. Obviously I would not recommend doing this due to the risks involved – get a competent sparkie friend to do this for you. You could do this while the pump is still connected just to check that it is the pump that is faulty.
I have just ordered a replacement from shop.ezee-fix.co.uk, part number AEG Pump - AEG8996464036582 for me. I hope it arrives soon as my hands are getting a bit soft from all the washing up!!
Good luck
Nev
April 2009