Yup - bad connection(s) or wire - you're washing could be totally coincidental. If you have to wait for the snow before messing with this, then I'll assume it's outside - yesterday was single digits here. Cold weather and starts will find every weak wiring component.The starter starts to click, then just dies. All other electrical functions work. The battery is new.
I'll bet the starter is fine - try the jumper cable thing I described before - if the battery is good and the motor isn't locked up, then it will turn over.