Kenmore 57033 Water Dispenser Broken

Are you sure the water (solenoid) valves are actually working? You should hear a distinct 'click' when they're activated. If you remove the outlet tube from the water dispenser valve, does it pass water when activated? Have you checked that the solenoids are actually getting voltage on demand?

Your water control valve is defective and will need to be replaced. Even though you hear the electrical part of the valve turn off the mechanical part of the control valve is stuck open causing water to continue to flow. What is your model number? Kenmore model numbers look like this example=> 312.234567 If you can find your model number I will show you the replacement part number, Thanks Sea Breeze

When you press the handle, do you hear/feel a click?
Is this just starting to happen after a power outage?
Is the ice machine making ice? Dispensing?

Do you have/know how to use a multimeter to check voltages at the water valve solenoid?

Thanks!

when pressing in on the water dispenser you should hear a clicking sound from a micro switch being activated. if you hear the micro switch clicking ok then you'll have to disconnect the water at various points and retry to see which locations the where water is coming out and where it is not. Trial and error approach to narrow down the problem location. usually either a bad water valve or a freeze up in the water line somewhere. assuming water is working to icemaker.

Probably the plastic tube that came from the solenoid is broken somewhere between the solenoid and the dispenser(usually under the refrigerator).

Sounds like a plugged water filter, assuming the water is turned on to the fridge. If you have a manual, refer to the section about water filters. The filter is usually accessible from the front of the fridge at the bottom....requires about a 1/2 turn counter-clockwise. Some units require that the water be turned off first but not all.

If you do not hear a click when activating the dispenser, there could be an issue with the water solenoid (water valve) that opens and closes when you use the water dispenser....agai...check the manual if at all possible.

I had a similar problem on a frigidaire side by side. I think the water line may be freezing. My solution was to remove the filter inside the refridgerator and drain it and reinstall. This causes the water to flow into the filter and eliminates any ice in the tubing. I have not had the problem in a while. While not a true fix, it may help narrow it down.
Later on, I eventually replaced the microswitch on the door dispenser for an intermittent dispenser problem.

Hope this helps.

Water dispenser is a simple touch switch in door energizing a solenoid water valve behind ventilation grate above refrigerator. Water tube runs down into and ends at ice dispenser chute. Should hear solenoid click at top of fridge when activate water touch switch. Can unhook discharge side of solenoid valve temporarily to prove water output. If water dispenser tube acts blocked it could be frozen where it ends-look up the hole at the bottom of refrigerator control buttons.
Ice maker is totally different system. No clicking when push ice button but ice in bulk tray may mean the simplest of malfunctions: Ice bin not pushed in the last half inch if ice auger not lined up with drive pegs. There are hidden switches behind ice bin that need to be engaged or nothing will happen in the ice maker: no auger noise, no clicking, no new ice making. Ice bin will be flush with sheet metal if it is in the right spot. Also plastic juice rack won't hang properly if ice bin not pushed in all the way.

no water come out of dispenser to glass

This is Gene's solution not mine, for a Ge fridge.
Assuming the ice dispenser works fine, the first thing I would check is the water filter, then the water inlet valve on the back of the fridge.

If the water filter is more than a year old it will cause restriction to the water flow.

Locate the water inlet valve on the back of the fridge. Remove the wires from the blue solenoid and check for 120V coming to the solenoid while the water dispenser lever is depressed.

If there is 120V then the water inlet valve has to be replaced.