It sounds like to me that someone has fitted an electric washer conversion and left the little schrader-valve hose connected - if you have an electric pump, you don't pressurise the tank, the electric pump is there to do that for you.
If it IS a conversion, then the washer button will have a tiny switch inside it. You should have someone with vehicle electrics knowledge take the switch out and test it. The first thing to do, is take a look at all the fuses, and see if there's any that are blown - IF (and this is a big IF) the washer switch was wired back to the fuse box, and not just connected to terminal 30 on the light switch as a lot of people seem to do (it's dangerous, ask me how I know).
If it's NOT a conversion (therefore an original system), then it's possible the seal inside the switch (*which is not a switch but a valve) has gone bad and is stuck open. The switch (sorry, VALVE) would need to be replaced.