Water tube broken under fridge

Only if its a push fitting ? ir not just cut the leaking pipe out and join it with a connector

Sounds like the water tank in the fridge section froze and split open causing a leak. Plus, the water feed line to the dispenser has frozen where it runs up through the freezer door- guessing your trimmer line only goes about 5" into the tube?
There is a water line heater kit that GE makes : Refrigerator Heating Element WR49X10173 .
Then, buy two quick disconnects 5/16" and about 10 feet of 5/16" plastic tubing- use the tubing and disconnects to replace the cracked water tank and you should be good to go... Refrigerator Water Line 5210JA3004K

I am wondering about the hose you shoved in and the leak stopped. Is the hose you pushed in buckled where it hooks on or is there a buckled spot where the water comes out of the fridge. Just a guess.

Two possibilities:
1. A cracked plastic tube. These will leak whenever there's a call for water - either the chilled water dispenser, or re-filling the icemaker tray (two seperate tubes). Pay particular attention to anywhere the tubes are clamped to the chassis; anywhere they're routed near or under the refrigeration unit; and near the solenoid valve - especially if there's a tight loop in the tube there.
2. A bad (leaking) connection where one of the tubes exits the water valve. Again, these will leak whenever the valve is activated.

Those plastic tubes don't last forever. I've replaced many of them for the same symptoms. They're known to simply deteriorate with age.
Manuf's make good money selling replacement tubing kits.

Make sure it has water on the container and no obstruction on the water dispenser. Try several times. Since it was new unit, sometimes water has not yet completely fill the dispenser tubing hence it will not dispense water.
Look for some carton, foam or plastic obstruction around the dispenser, it may cause hindrance of not flowing water from dispenser into the glass.
Thanks for asking.

It could be the water valve side for the dispenser. So a couple of problems can be had with this description. 1. The electric solenoid for the valve is bad so it doesn't open the valve. 2.The valve itself could be bad so the solenoid opens it but nothing flows. 3. The water line could be frozen inside the door so no water flows. 4. The dispenser switch is bad or the plastic holder that holds the switch is bad so the switch fell out of its proper position. 5. The circuit board is bad.

Easy way to check is to pull out the fridge and take the water line off that valve by pressing down on the little ring around the line while pulling up on the line (tube thing). It should pull out easily(to reinsert just push the tubing back in without holding the little ring down, it goes in by itself and self-seals). With the tube out of the solenoid valve have someone operate the water dispenser lever and see if water shoots in your face ha ha. Read further if you're testing by yourself...

You can also do the same test from the front underside where the tubing has a coupling just under the door hinge area (so you can take the door off without cutting the tubing). Pull the lower skirt off the front of the refer and you should see the tubing and little coupling, it works the same, push down on the ring area and pull the tubing out. That way you don't have to move the fridge and can operate the dispenser lever yourself to see if water flows out the disconnected coupling. If water flows then the valve/switch/circuit board are working fine of course and your tubing is frozen at the door. You will need to defrost the tubing somehow, usually means a hairdryer blowing up into the dispenser area or turning off the whole refer and leaving the door open for a day.

If nothing happens (no water still) then you need to check if the solenoid is working electrically. Pull the fridge out and pull the wire plug off the ice maker valve and put the wire plug from the dispenser valve on the ice maker valve. Watch inside the ice maker and push the door dispenser lever, if water flows into the icemaker then the electrical door switch/circuit board is OK and the problem is likely the solenoid valve to the dispenser is bad or a frozen line in the door still. You get the idea, you can swap wires/valves and even tubing (if their the same size) around till you logically find the part not working. Remember in troubleshooting you're not really trying to find the broken part... you're trying to find ALL the other parts are working, which by process of elimination will lead you to the last part that ISN'T working.

If you are comfortable with electrical troubleshooting using a multimeter you can check for 110 vac at the plugs when the switch is press also but that depends on your tools and skill level, etc.

See this link for a diagram of that door assy and the parts involved.

Typically I'd be suspicious of the valve itself being bad or the circuit board, next on the list is the switch, and last would be the frozen line.

You need to check for water flow. Is the water flowing when you try to get water at the door? Can you hear it running? If not than it is probably your water valve on the back of the fridge where all the water lines come together at the bottom. If you do hear water running, where is it going? Pull the fridge out and watch the back while you or someone else tries to get water.. You probably have a broken water line. If it is the water valve it is very easy to replace. Unplug the fridge and turn off the water to fridge. The cardboard bottom guard on the back comes off with a 5/16 nut driver. The water valve is blue and has two sets of wires hooked to it. Should also have a 5/16 screw holding it in. Remove the screw. Take a picture of the wires or label them. Unplug the wires and then the tricky part. The water lines come out by pushing in on a little ring right around the tube at the valve. Push in on the ring and while pushing in, pull out the tube.Go get a new water valve and do the reverse to install. Just push the tubes all the way in, no need to push on the ring again. If it is a broken water line then you will need to get more tubing and replace the broken stuff. Do not forget to plug the fridge back in while you get a new water valve or tubing! The wires will be ok.

The water line is broken somewhere from the water dispencer all the way down to the water valve. I usually find that it is broken next to the water valve. Hint: Water valve is blue and located behind the fridge in the compressor department. Water line is 1/4inch clear tube that is probaly now a "yellowish" color. Easy to spot, easy to fix, especially if located next to water valve...

check to make sure there is nothing blocking the water lines and no kinks in the water lines, you did not say if it had an ice maker, and if it is affected.
The frigidaires also has a plastic tube coiled under the back to dispense cold water make sure this tube is not kinked.
Hope this helps

Usually the coolness comes from a large coil of plastic tubing in the refer compartment that stores the water. Check that the refer compartment is cool enough. Also see if running a large glass or two becomes cool again and stays cool for a while. Usually the very first 1/2 glass may be warm until the "cool" water that is stored in the coil of tubing finally makes its way to the dispensor.