If the button is stuck in then its possibley the switch itself. For this you need to remove the plastic control panel.
Make sure the power is turned off and then open the door and remove the screws holding the plastic panel on on the inside.
Once thats off you can then access the switch. Its just clipped into the panel so use a flat bladed screwdriver and prise it out from the panel.
Then from there you can check the switch and see if it pushes in and out. If not then you need to replace the switch from there to cure that fault.
Then retry it and see how it goes. But if its still not draining then its possibley a blocked pump.
For this you need to pull the dishwasher out and remove the right hand side panel.
From there you will see the drain pump. It will have the grey drain hose going to it. You need to remove the pump and clear out any debris in there and make sure the pump is clear.
Then retry it and see how it goes. Fingers crossed this cures it.
But from the fault you describe i think it can still be fixed and quite cheap as switches are not that expensive.
If you need anymore info just get back to me.