The humming noise you hear is the wash motor trying to run.
I say 8 times out of 10 for this fault the wash motor itself is the problem.
What you can try is pull it out and remove the side panels and access the motor. Bolted to the side of the motor is the capacitor. Its either a white or silver cylinder with a few wires going to it.
What this does is gives the motor a boost to get going. Now sometimes this can be faulty and doesn't start the motor up so it just sits there humming.
What yo can try if you want is replace this first as they are about £10. If you are lucky it may just be this.
But if it still not running then the motor itself will need to be replaced to cure this which is quite expensive im afraid.
If you need anymore info just get back to me.