Sometimes what happens is that when they install a garbage disposal the pipe coming out of it ends up being lower than the pipe exiting the pea trap thru the wall under the sink. If it is a dual kitchen sink this is very common. Being lower than the exiting pipe causes water to stay in the bottom of the disposal and not just the pea trap. If you have a side by side sink in the kitchen and the water is backing up in the other sink also then more than likely the pea trap has a blockage. It is not common for the straight line from the pea trap going thru the wall to become blocked, but it does sometimes happen. The biggest cause of this is poring hot grease down the drain. It is just about the point that it cools enough, sticks and hardens plugging the drain pipe.
You probably should have a plumber look at it and make sure everything is running downhill under the sink. The only place that water should set in the plumbing is in the pea trap so that odor from the sewer does not come up into the house. Without actually seeing it, it is hard to tell exactly what is happening. The pea trap is easy to clean, put a really big pan under the trap, make sure you have emptied as much water out of the sink as you can, then with a big pair of channel locks unscrew the two nuts that hold the pea trap in place and let the fluid drain from it, then finish unscrewing it from the pipe. You can then clean it out and check the pipe thru the wall for blockage. When reassembling it, screw it all together loosely and then move the pieces around while hand tightening each joint so the they have no pressure on them, then use the channel locks to finish tightening the nuts. Don't over tighten them because they have nylon seals in them that compress to make the seal. Just tight enough to seal and not leak. You should be up and running again unless the plug-up is farther down the wall pipe. Good Luck, RAC

It just happened to me, Kept spinning and turning but no draining. I read all the online recommendations which sounded very hard. I got as much water out as I could. Then spun it again and collected more water with a soup ladle. Then I poured boiling water down it and capped it and went to the store to buy Drano Max Gel which is good for disposals. Took me about 20 minutes. Got back and turned on the disposal keeping the cap on and then it drained....did not even need the draino max gel. too bad I threw away the receipt on the way out the door. this was alot easier than taking apart the u pipe or whatever people said we had to do