Edit: Similar happened to the same machine in 2024, this time it was a small o-ring in between the thermoblock and the plunger. This video helped me significantly after I found a bit of rust on the plate under it.
I purchased a second hand Delonghi ESAM 03.110.S coffee machine since I was given a Delonghi ESAM 3400S, replaced the boiler when I realised it started leaking and loved the challenge of repairing it and started using it every day.
The Delonghi ESAM 03.110.S did’t have any water coming out of the spout when trying a rinse or making a coffee. The steam wand had hot water, and steamed (but only for a short while before stopping).
I had taken the machine apart and checked for blockages and ran descale a few times. We’d used citric acid and used the rinse and hot water and steam functions a LOT of times to see if it helped. We swapped over the infuser from my other machine to make sure it wasn’t that. The machine had no rust, and was VERY clean inside and out.
When pressing the button to make a coffee, it seemed the coffee was ground correctly and the unit moved correctly, but instead of water being pushed through the coffee grinds, a small amount of water got pushed out the steam wand and then the machine cleaned off the grinds and ended the cycle with no coffee being extracted.
I posted this on a coffee forum but after several weeks received no help at all.
In case this helps anyone, I managed to fix this machine. After taking bits apart and cleaning them, I found that the steam wand had a broken o-ring. It was fairly difficult to get to, but pushing against the side on a bench, the pieces came apart. Once replaced, this machine works very well and have been using it daily ever since.