I just fixed a similar problem with my Delonghi Eco 310. Halfway through making a cup water stopped coming out but ran out from underneath.
This is how i fixed it:
First I checked the little tube that goes from the pump and anti drip valve into the boiler unit. There is a clamp on both ends to remove before you can take it out. First fault can occur here, check the black little O-Rings that might still stuck inside the connectors, if they are worn out they might need replacing.
Then check the little tube for any damage, even any fine tiny cracks can lead to a big leak as 15 bar go through it.
In my case there was no damage there, also not on the tubes that come from the watertank into the pump.
After I checked all that and it seemed fine, I turned the machine back on again with open top (careful of any electrical contacts!!!). Then I saw that water and steam came out of the anti drip valve. It seemed the water got sucked into the pump, pumped into the boiler, heated up there and put to 15 bar, but because the valve was broken the water didnt actually came out but searched the easiest way, which was the broken valve, that regulates the pressure. I went on a site for delonghi spare parts, bought a new valve for £5, replaced the old one and -tadaaaa! It works again!