Delonghi EAM3400 water ends up in tray will not come out of spout
i had this problem, and have now finally figured it out and fixed it. the problem is that there is a solenoid valve sticking. i believe that the valve is used to relieve pressure after using the steam, and it vents the hot water directly to the tray. if you aren't diligent about descaling, or if there are water impurities, or if you use the machine infrequently, or for probably any number of other reasons, the valve can gum up and stick in the "open" position, continuously draining the water directly to the tray.
one easy way i've got my machine to work was to cycle steam on and off a few times, thereby signaling the valve to open/close, and unsticking the valve. you can see if it worked without wasting coffee by initiating a rinse cycle, and seeing if the water correctly comes out of the coffee nozzles.
if that doesn't work, you can disassemble the machine and tap on the valve. it has a square black solenoid ~1" square on top of a brass valve. it is mounted on the same bracket as the u-shaped heater. a few sharp raps on top may free up the valve.
if that doesn't work, remove the valve, and try to blow through it. if the valve is stuck open, air will go right through. hold the valve upright and tap it onto a hard surface (countertop, floor, etc.) try blowing through it again. when the valve is unstuck (and held in its normal operating position), you will not be able to blow through it.
once the valve is unstuck, run your machine through a descale process. that should take care of it.