I had exactly the same problem with exactly the same washing machine. I opened up the pump and found about 4 coins a couple of hair bands and just general fluff stuck inside. Once I cleared that out the pump it can drain the machine. If the machine won't drain then the spin cycle will not kick in. I would guess that you have extra stuff stuck inside your pump or some more stuff stuck in the draining tube.
WORD OF WARNING if you take your pump apart (as I did) it breaks about 6 seals and now my washing machine leaks so much that I am going to have to replace the pump. doh!
anyone know where I can get a pump for a candy aquaviva 1300
ps. some washing machines like being level, if they are not level the spin cycle won't start otherwise they jump around the room more...so you could try that.
Guy mitchell, June 2007