Water not dispensing from a Samsung SRS615DP but ice working ok

You have 2 separate valves, 1 for the water dispenser and 1 for the ice maker. (otherwise your ice maker would overflow every time you got water from the dispenser and your dispenser would flow every time the ice maker went to refill.) They are fed from the same tubing.

The cube/crushed ice motor is completely separate from the ice maker itself and should have absolutely no bearing on the water flow.

You have narrowed down the problem quite nicely to the ice maker water valve. There is one more thing to check though, the connector. There should be a multi-contact connector from the ice maker to the back wall of the freezer, usually 6-9 wires. Pull that apart and check the cord side (ice maker side) for any corrosion. BE CAREFUL NOT TO TOUCH THE OTHER SIDE AS THERE IS LIVE 110V!!! If you don't see any corrosion, still try try disconnecting and reconnecting 5-10 times and see if that solves your problem. If you see corrosion, unplug the refrigerator before working on the back wall part of the connector. [This connector besides powering the ice maker also allows the ice maker to control the water valve which can't be inside the freezer]

Maybe and maybe not.
Page 9 of the user manual mentions a anti sweat heater that you can turn on or off.
Samsung SRS579NP User Manual Ice cold Water Dispenser

It maybe that the water line to the water dispenser is leaking
I am including a link to youtube videos about refrigerator water leaks but there is little about Samsung. Hopefully turning on the heater will solve your problem. At least one of the videos shows how to replace the tubing in a different brand of refrigerator.
samsung side by side water leak from freezer door YouTube

disconnect and wait for full melt down. then reconnect

check the water line fron filter that continues on to water dispfrom icemaker, also a bad water disp solenoid or no pwr to water valve disp solenoid could be a problem,when you try to disp water can you hear a click from the solenoid operating to let water out?

switch or water valve

you would have to start with the water supply.
check if you have water coming to the fridge.

close the tap going to the fridge, open the line to the solenoids and open the tap. if there is water then supply is ok.

next check if there is power going to the water solenoid . ( this is different from ice maker solenoid) be sure to know which one.

press the dispenser, there should be power to the solenoid and solenoid should click open. if there is none, electrical problem is present.

last thing to check is the micro switch in the dispenser.

it should have contact when you press the dispenser.

tnx 4 using fixya,

drcool

your fridge is slowly icing up, you'll next notice the fan being noisy. read this article and ring samsun on the free phone number

http://www.bbc.co.uk/consumer/tv_and_radio/watchdog/reports/consumer_goods/consumer_20080407.shtml

there is a double valve at the back bottom lhs. check continuity of both valve coils but doubtfull this is the problem. the fault may be that the filling tube is frozen. try looking in this area