My garbage disposal has about 2" of water in its sink that won't drain. The disposal itself runs, but the water doesn't drain. No water comes up the adjoining sink. We've plunged it but that hasn't worked. Any experience or suggestion re this type of problem? Thanks in advance.

Remove the drain from the disposal and check there. Check the drain and looin the disposal there. Maybe put a bucket under it a try and flush it out

Try disconnecting the drain pipes under the sink, start with your traps. Have a bucket ready.

Not knowing any more than I do about your situation I have to assume some things or ask questions. You say no water comes up in the adjoining sink, does that mean that you have two separate drain lines going into the wall, one from the disposal and one from the other side of the sink. If this is the case it is possible that your lines connect under the house to form one line again. If this is the case they also connect again in the wall to form one vent for both drains. And if you run water into your disposal and it drains all of the water out except the 2 or 3 inches that is in the bottom of the disposal, this could be because there is a stoppage in the line from the disposal leading to the connection under the house, therefore the disposal will not drain by gravity flow but when turned on it will pump the water up and out the pipe in the wall over to the pipe that goes to the other side of the sink.
All of this is only supposition because of the info you gave was not very detailed. I hope you can understand what I was trying to explain to you. And if what I said is true you need to disconnect the trap from the disposal and run a drain cleaning cable down the pipe until it unstops. Let me know if this helps you and please rate my answer.

I know this seems so simple but after having the same problem with my garbage disposal drain not draining yet working okay I found on another site to simply plug up the other side's drain and run the disposal. It cleared and the water went down after about 45 sec. We tried all kinds of stuff prior to that and were getting ready to call a plumber when I found the suggestion.