After starting the cycle, the dishwasher starts and runs normally for a short time, then the water drains out of the tub prematurely while the cycle is still going. The machine then runs dry until the cycle times out. At the next cycle and the process repeats. It started as a sporadic problem, but is getting worse.

The hose could be clogged or an issue with the valve assembly.Or something being stuck in the inlet water valve. Check to see if there is any problems coming from where the water enters into the tub for your dishwasher mostly on the left side wall of the tub on your dishwasher.

You either have a bad water valve, or a bad case-brake assembly (in which case you should have an error code or blinking light on your console).

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Not enough information, are you stating when you start the cycle no water enters the tub?
The normal operation at start the washer goes into drain first then starts the cycle.

The wash cycle starts with the pump running to drain residual water from the tub. Make sure your drain is clear before starting each cycle. I run my garbage disposal with water on for a few seconds before starting the DW. If I don't it won't drain properly with food waste in the disposer basket. You may also need to pull and rinse your drain sump screen (front right corner). Just snap it out and rinse. If your machine doesn't power up at all you'll need to use a sponge to drain the tub

If there is a lot of water sitting inside the applicance, it's possible that the high water float switch has been activated and is preventing the dishwasher from running. Open the door, remove the bottom rack, dip as much water out of the bottom as possible with a shallow ladle or even tupperware container. When that is accomplished, shut the door and try to run a drain cycle. If the unit won't start, you may have to remove more water. You don't have to have the rack in place to run the drain cycle.

Check the float switch inside the tub, it should move freely up and down.

Check the harness to the motor

Check start capacitor on the left side of the wash motor

The float switch in the tank is bad,also if water only trickles in your fill valve is going bad which will not let it fill all the way to start wash cycle. Fill tub with pot of water to raise float, if wash cycle starts,replace fill valve,if not,replace float switch.

Are you sure your drain system is not clogged or restricting water flow ? When you say youtook off the hose off under the sink and it seemed to be lots of water running on the rise cycle .. that suggests that you may have a restriction after the drain hose in your house drain system. ...

Some other considerations..

To minimize the possibility of electric shock, unplug this appliance from the power supply before attempting any maintenance.

• Some water, usually one to two cups, remaining in the bottom of the tub is normal. However, if water is covering the bottom of the tub, the dishwasher is not draining properly.
  
  
• Check for paper or large objects covering or blocking the sump area in the rear of the tub.
  
  
• Make sure that the right type and amount of detergent is used: Using the wrong type or too much detergent can cause sudsing that can prevent the dishwasher from draining. Only detergent specifically designed for automatic dishwashers such as Electrasol®, Cascade® or Cascade Complete® should be used

Hope this helps you...

Check disposer plug. If a garbage disposer has been recently installed, it is possible the disposer drain plug was not removed. The drain plug is a plastic piece in the disposer that blocks the hole where the dishwasher hose connects. Also check the hose connected to the disposal. Mine apparently had a kink in it. When I straightened the hose the dishwasher drained at full speed (I recently had a plumber re-route a hot waterline. He must has bent the hose). Hope this helps. If not go to the GE website. That's where I found my answer.