My new GE gfws3500lww keeps on pausing when I start up a cycle.

Either the drain hose is or the pump could be clogged or plugged.Or it needs a new drain hose or a new pump for your washing machine.

This part is very expensive http://www.appliancepartspros.com/ge-control-board-asm-wh12x10485-ap4981003.html

no, there is no reset button. Make sure you are getting the appropriate voltage going to unit. If you have the proper voltage, it would either be a main control board issue or a wiring harness issue.

PAUSE? If you stop the dryer before it is done completing the dryer cycle you have paused it.

Does it stop filling if you stop the cycle or do you need to turn the faucet off?

The PAU, or pause, error usually means that the washing machine cycle was interrupted and was not restarted properly. If you try to modify the cycle or start a new one before the first cycle is complete, the PAU error will appear on the display. If the washer was stopped midcycle and not restarted, the cycle must be canceled or completed before a new selection can be made. Push "Start/Pause" to allow the current cycle to finish before making a new selection, or push "Cancel" to stop the current cycle
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Please, check to insure that your washer is properly grounded. If you do not know what that means, call an electrician. Modern wash machines are controlled by circuit boards that operate on low voltage and are vulnerable to static electricity. Spikes or gaps in the electrical service from your power company could also be the problem. Your electrician should be able to help you with that as well.

Is the door lock button on, but the door not actually locked? Our door lock switch keeps going out. We have replaced it 4 times in the last 3 years.

Washers - Resetting Electronic Controls on a Washer

If there is a pause in the washer cycle, the controls will lock up. The pause can occur because of a power failure or it was put in the test mode at the factory.

Also, if the washer was stopped before the cycle was complete or the consumer has pushed the stop/pause button to temporarily stop the cycle and the cycle is not reset. Over a period of 24 hours, the washer will pump out and spin, but will stay in the final spin.

To correct the situation, shut off the circuit breaker for 30 seconds or unplug the washer, then turn the timer knob around and back to any position other than final spin. Verify the water is turned on and restore power. This should resolve the issue.

http://www.instructables.com/id/GE-Adora-Lint-Filter-Cleanout/?download=pdf

Had the same problem, this fixed it!