How do I get water to come out of my Bunn coffee maker?

Normally that would be an easy fix if the water just continued to flow. You just replace the water inlet valve and they can stick open or partially open. But you say if you power off, the flow stops. That sounds like the control board is supplying residual power to it. Control boards are expensive so I would call for service. Or you can try some of the fixes here.

https://www.google.com/search?q=bunn+coffee+maker+cwtf15+replacement+water+inlet+valve

More here

https://www.google.com/search?q=bunn+coffee+maker+cwtf15+water+not+shutting+off

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if the coffee is ground too fine, it'll take longer to brew through. either grind more coarse or call bunn for a flow restrictor (800) 352-BUNN (2866)

the fill drain is plugged and the water is overflowing. open the top and, using a phillips head screwdriver, poke through the lime buildup in the trough drain until the water goes down more freely.

delime the sprayhead and the reservoir drain in the top with a deliming spring or a screwdriver

The metal proble is use to clean out the water tubing. Remove your sprayhead and insert the metal rod up in the hole leaving out about 1-2 inches. Then simply twist and turn the rod about 5-6 times. This will remove any lime deposits. Then flush out with 2-3 decanters of water. You can obtain a new manual by calling customer service or going to the website-www.bunn.com going to @home, then products-click on your brewer-and then select use and care manual and you can print it out or view it online.

Dunkin Donuts is a finer ground coffee and the water comes through so quickly that it isn't absorbed quick enough so you don't get the full flavor and it causes an overflow. If you will call Bunn Customer Service, a new flow restrictor can be sent to you to resolve this problem.

Tressia,
An overflow can occur when using certain brands of coffee that are finer ground or using a water softener, bottled water, reverse osmosis, or filtered water. If you will call Bunn Customer Service, you can get a flow restrictor sprayhead which will eliminate this issue.

Try this open faucet to make sure water is flowing to the machine, then remove the pour over cover and pour in water until it flows through the sprayhead, then turn brewer on.

Some people also try adding fresh grounds to brewed grounds, resulting in an overflow. A restricter valve can be used, but a better solution is to simply pour in half the water at a time. This is what people who buy non Bunn filters do to stop overfills.

You may be grinding the coffee to fine making the draining a little slower. There's something called a fast flow filter that may help also. Also, make sure that you aren't jamming the filter down to partially block the drain hole ensuring that it is freely draining out unobstructed