How can I repair a leaking valve on an unused refrigerator water line?
You have two possible leak causes, so you need to separate them to figure out which one it is.

I assume the line to the old ice maker is still running behind the fridge.  Rather than just shut it off under the sink, disconnect the line under the sink and put a tray under the valve to catch any drips.

The next day, check the tray for drips.  If the valve has been leaking, you can cap it off or you can replace the valve with one that doesn't leak.  A cap is going to be cheaper and faster if you don't intend on using the ice maker line in the future.

If there are no drips in the pan, but still a puddle under the fridge, the fridge is probably missing it's condensate drip pan, especially since it was sold from an outlet store.  It's normally a plastic tray that slides under the fridge.  Water drips into the tray periodically and then evaporates.  If theres no tray the water can flow out from under the fridge and make a puddle.  The outlet store should be able to confirm if your fridge requires a drip pan and probably help you order a replacement (tho you may have to pay for the part).