When I run the water dispenser there is a water leak on the floor.

Question edited for clarity.

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It's not unusual for a refrigerator to drip a little water on the floor after you replace the water filter-air trapped in the water dispenser system can make the water dispenser drip enough to overflow the drip tray below the dispenser. You can fix it by streaming a gallon or two of water through the dispenser to eliminate the trapped air.
If water drips on the floor from the back of the refrigerator, a leaking water inlet valve or cracked water system tubing could be the cause. A clogged or cracked defrost drain tube could also cause the leak. Defrost condensate water collects in the drain pan at the bottom of the refrigerator so a cracked or overflowing drain pan can also cause water to drip on the floor behind the refrigerator. Check the drain pan for cracks and clean out any foreign objects that may be inside the drain pan.
Excessive frost caused by a leaking door seal can also cause the defrost drain pan to overflow. Check the door gaskets and replace them if damaged.

On the bottom rear of the refrigerator as you are looking at it from behind the left side where the water is feeding into there should be a double valve. 1 is for the water and the other to the icemaker. Many times that valve won't shut off, however the switch that dispenses the water is evidentially bad and needs to be checked if it is stuck open.

Just bought an off the floor LG fridge model number LSC27914SB and when I turn it on it beeps. Why is it doing that?

Hi

Under some circumstances the water dispenser can leak water into the spill trap when not in use. This problem could be caused by one of several scenarios involving the installation of the refrigerator doors. Small leaks are often triggered when a new water filter is installed. The exact location of some parts will vary depending on your model of refrigerator.

Keep a glass under the dispenser for up to three seconds after releasing the lever. The water doesn't cut off immediately, and there may be a few remaining drops in the system. This is normal and doesn't need any further attention.Run the water dispenser into a large container for three minutes. Empty the contents of the container down the sink. A newly installed water filter may spurt or leak water from the dispenser until the water is run for a few minutes. Some dispensers may cut off after a few minutes automatically.

Run the dispenser intermittently -- five seconds on, five seconds off -- for two minutes. This measure clears air trapped in the supply line, filter and dispenser system. Some dispensers will spurt or leak water until all air is purged from the system. You should follow this step each time the water is disconnected or the filter changed.Ensure all components of the water supply have been properly connected. All connections should be tightly screwed in place and pipes straight so water doesn't leak out of the pipes or dispenser nozzle. Contact a technician if you didn't install the refrigerator yourself.

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You models has a tubing coil as a water tank. Once you changed the filter air bubbles remained in the system. Slow leaks or drips from the water dispenser can be the result of air trapped in the water line and will usually occur just after replacing a water filter. When the filter is changed, a large amount of air enters the system and needs to be removed by running water from the dispenser until all the air pockets are gone. Another reason is the water valve itself may not be sealing when closed allowing water pressure from the supply like to work its way into the dispenser water line. This is a less likely reason, but you should be aware of this possibility when diagnosing your own problem. Thanks, Sea Breeze

Good day,
The hum is normal. That's the water valve in the rear of the machine being activated.
Lots of plumbing to be checked.
Water line starts at the dispensing outlet in the door, and runs thru the door to the bottom of the hinged side.
From there it goes to the filter,
'From there it travels under the machine into the cooling reservoir mounted back of the fresh food section behind the crispers.
From there it travels back out and runs to the water solenoid mounted on the back rear of the machine.
One of these lines or their fittings has failed.
It's a look-see repair.

Also, there is a remote chance the water line running inside the freezer door froze, causing this problem, and would require the machine be shut down (unplugged) and the door be allowed to defrost completely.

The most likely reason for the leaking at the water dispenser is the dual water control valve on the back and near floor is leaking water while shut off. The only option is to replace the water control valve. Sea Breeze

i'd shut off the water take apart and clean change water filter.

remove and reinstall water filter, possibly o-ring got sideways during installation.