Detergent dispenser tray not draining water after cycles

You can drain the detergent tray and clean the tray specially the area where the dispensing nozzle is place, use a air pressure or a jet wash, which must clear the fault as it can be due to dirt accumulation..

Was the dispenser cup wet when you added detergent?
Make sure the dispenser cup is dry before adding powdered detergent. If dispenser cup is wet, the detergent can clump.
Is the cycle incomplete?
If the previous cycle did not complete, the detergent can become caked in the dispenser cup if it is left sitting in the dishwasher.
Is the detergent old?
Older detergent exposed to air will clump and not dissolve well, which will cause the dispenser door to stick to the detergent. Replace detergent if necessary and store the detergent in a tightly closed container in a cool dry place.
Is the water temperature too low?
For best washing and drying results, water should be 120oF (49o C) as it enters the dishwasher.
Were items blocking the dispenser that kept it from opening?
Items blocking the detergent dispenser will keep it from opening. Make sure water action can reach the dispenser.
Detergent guidelines

• Use automatic dishwashing detergent only.
• Other detergents can produce excessive suds that can overflow out of the dishwasher and reduce washing performance.
• Store tightly closed detergent in a cool, dry place.
• Fresh automatic dishwasher detergent results in better cleaning.
• Add detergents just before starting the cycle.
• The amount of detergent to use depends on the hardness of your water and the type of detergent.
• If you use too little, dishes won't be clean.
• If you use too much in soft water, glassware will etch.
• Suggested fill amounts are for standard powdered detergent. Amounts may vary if you use liquid or concentrated powdered detergent. Follow instructions on the package when using these detergents.
• Water hardness can change over a period of time. Find out your water's hardness by asking your local water department, water softener company, or county extension agent.

If no holes are in the detergent dispenser which shouldn't be hard to see if any exist then I would assume that you may be adding too much detergent. Also remove the detergent compartment and make sure there is no build up anywhere that may be blocking the flow of the detergent.

Water floods the dispenser compartments at the start of the cycle to dilute/dissolve the softener, bleach, and detergent. The reason why water is in the compartment after the cycle is that, the detergent, the softener, and/or the bleach does not flow into the tub properly. It's either the dispenser assembly is clogged or excessive amount of detergent, softener or bleach is used. Clean the dispenser assembly and make sure to use no more than two tablespoons of powdered HE detergent or one-and-a-half ounces if liquid HE detergent.

1. Unscrew the two screws on the back of the top plate then pull it back then upward.
2. Pull out the dispenser drawer.
3. Unscrew the two screws then push the dispenser assembly out.
4. Unscrew the nut at the lower part of the dispenser.
5. Remove the four connectors from the valves.
6. Unscrew the two screws from the back of the cabinet.
7. Reinstall the dispenser assembly in reverse order.
   

Yes the system is cloghed. Pull the detergent drawer out and clean the drawers housing. try using some bleach. It allways helps.

BE ADVICED: after using bleach run quick wash cycle on without any load, it's just to get rid of all bleech remains and not to damage your clothes

Update me about your progress

check to make sure water lines are not clogged and detergent tray is not caked up

Is water left in the dispenser at the end of the cycle?
About two tablespoons of water remaining in the dispenser compartment at the end of the cycle is normal. At the end of the wash cycle, fresh water automatically cleans the dispenser. Check that the cycle is complete before opening the dispenser drawer.
Is the dispenser drawer clogged?
A clogged dispenser can block the flow of water through the dispenser and cause water to leak out. Manually remove the dispenser, and clean any leftover detergent or additives that could clog the flow of water through the dispenser. Also, check that the detergent drawer is always completely closed during the cycle. If the drawer is not closed completely, water can leak out onto the floor.
Are the additives dispensing too early?
Here are a few things that can cause the additives (detergent, fabric softener or liquid chlorine bleach) to dispense early:

• Check that the dispenser is not overfilled. Do not fill past the MAX fill lines on the dispenser. Overfilling can cause early dispensing of liquid chlorine bleach and/or fabric softener.
• Check that the detergent separator is in the correct position. For liquid detergent, the separator should be in the front position. For powdered detergent, the separator should be in the rear position. If the separator is in the rear position while you are using liquid detergent, it will dispense immediately, which is not how it is designed to work.
• Use powdered HE detergent when using the DELAY WASH option. Liquid detergent may dispense prior to the start of wash.

Are the additives dispensing too late?
The additives will not dispense until the proper time if the DELAY WASH option is selected.

Open dispenser drawer and push down on center plastic tab at back of dispenser to allow you to take dispenser out of machine. Take the plastic pieces off and clean them. (they need to be clean in order to siphon the bleach, softener, etc out. If there is water left in them, the water fill valve is OK. Cleaning should fix your problem. If you are using concentrated additives, try diluting them a bit with warm water when you add them to the dispenser. Remember, only one tablespoon (max) detergent, one teaspoon (max) fabric softener per load.

I think this is normal. Mine does too.

Remove dispencer again, remove conditioner syphon assembly and clean up the little tube. Should then go okay