I have the same problem and its very fustrating and I have woods floors also. How did you turn off the water? I do not want to use it anymore cause when the ice cubes fall on he bottom (which is all the time) they melt and water literally pours onto the floor so I would rather not even use the ice maker anymore.
We thought it was ice at first as well but it was the crappy fridge. You need to back off the levelling feet in the front and roll the fridge out. The turn off the water supply. If you are lucky the shut off for the water is somewhere else other than behind the fridge - look for an access panel somewhere close to the fridge first before moving the fridge out.