Here are your parts
Replacement parts for AMANA ADB1200AWW | AppliancePartsPros.com

Here is a tech sheet and a service manual
http://www.servicematters.com/m...ibrary/docs/16023224.pdf
http://www.servicematters.com/m...ibrary/docs/16021814.pdf

Try the diagnostics.
If you do not have a meter you may want to purchase one, see below.
Is the main motor making any noise at all (humming)
Check the motor with a meter using ohms.

are there separate drain and circulation pumps?
Yes

Is this something that a reasonably handy (but no real experience with dishwashers) person can fix?
Probably

Or should I hire a repair tech? Or buy a new machine?
I would do some basic troubleshooting first and try to do the repair. At the very least you should be able to narrow down the cause and then can decide if it is worth putting the dollars into it.
With the above info you should be able to fix it yourself.

METER
If you do not own a meter, I would suggest you purchase a one. You can get a decent digital multimeter for under $20.00. You do not need fancy though it is nice if the leads are a couple feet long.
If it saves ordering one unnecessary part it has paid for itself and you end up owning a useful tool.
Most places will not let you return electrical parts so if you order it, you own it.
A couple things to watch when measuring ohms and continuity
1. Always remove power from the machine otherwise you could blow your meter.
2. Always disconnect at least one side of any device you are checking. This eliminates the possibility of measuring an alternate/parallel circuit path.
3. When checking for closed contacts and continuity use the lowest scale (Usually 200 ohms). Then try higher scales. This scale is 0 to 200 ohms so if the device you are measuring is 300 ohms this scale would show an open circuit which it is not, you are just measuring outside the scale's dynamic range.

There is a good STICKY at the start of this forum about it's use.

I have an Amana ABD1200AWS and the same thing is happening. I thought something was jammed, cleaned everything out - found some pieces of broken dish. Some water comes out in the bottom - impeller is spinning - but not enough force to send through all arms. Maybe the motor gears are stripped? How did you troubleshoot the impeller problem. Denman, can you post the docs for my unit? Thanks.

Yes Denman, you are correct on the part number. I just discovered the problem. The plastic stem which screws onto the threaded post coming up from the motor is stripped. The chopper goes onto this step and then the impeller slides down on top and is secured with a screw. i think that the small piece of the dish that my wife broke (that I found near the chopper) must of jammed the chopper and impeller which caused the plastic to get stripped by the threads - in other words, chopper stopped, motor kept going. The motor appears to be fine. It was just spinning and slipping at the same time, causing not much water to be picked up by the impeller, causing the spinner to not spin with water. This also explains why some of the soap was not getting properly rinsed off of the glasses on the top shelf. The part is $24. I'll post the results after the repair is done. Thanks.