Where to find a dispenser holder for Gaggia Syncrony logic

The unit requires a new grinder assembly

Check the 2 thermal cutouts located on the side of the boiler
Press to reset

Check the chamber under the white plastic valve behind the brew unit, it might be blocked with coffee.

Check the site at importika.com they have a list of repair areas any one of them will have a spout in stock.

Yes the machine should not be left on for that long, it only takes a few minutes to heat up. It does not have an auto refill if the boiler is low on water.
If it heats up the water in the boiler for over an hour, it is safe to assume, that the water might at some point turn to steam, when you use it for the first time, it flushes out all the steam, and fills the boiler with water.

Lubricate the brew unit with a food safe grease this should help.
The brew unit becomes stiff and fail to load up fully this stops the water being dispensed

It sounds like you need to program the coffee level.
Have a look on this page for the instruction manual.
http://www.coffeeitalia.co.uk/downl-manual.php

You can check with wholelattelove or servicesunlimited.

Try this press the button for ground coffee then when it lights up press the coffee brew button, if water flows normally then the grind on the grinder needs to be adjusted coarser, if no water then the screen on the brew unit is blocked.

I need a manual also.