Spray Tower The spray tower to my dishwasher came off.It is part of the filter module. I have no idea how, but when I look at it, I can't figure out how to get it back in place. It is from a Whirlpool DU920.

If you are speaking about the filter behind the spray arm in the tub:
grasp the tower (the top post above the spray arm)
and unscrew it. CCW under and in the center of the tower hole thus revealed is a philips screw and fiber washer holding the spray arm on remove these then remove the arm. next, using a flat screwdriver un-snap the filter cover

Hi, you may want to try looking at all the holes in the spray arms. If you see anything blocking a hole, use the tweezers and remove the stuff.
Remove the bottom spray arm and check for items in the water delivery hole.Check the lower spray tower that is connected to the bottom rack. Make sure all rotating parts rotate properly. Look underneath to make sure nothing is stuck in the tower. Remove any stuff stuck that is preventing rotation or clogging the tower.

there is something clogged in the motor/pump or its intake

Steps:
1)Shut off power to the dishwasher at the circuit breaker and turn off the water line to the dishwasher by locating the shut-off valve, which is typically inside the cabinet beneath the kitchen sink.
2)Remove the four screws that hold the dishwasher kick plate in place.
3)Locate the motor,which is typically centered beneath the bottom spray arm.
4)Lower the dishwasher door and take out the bottom dish rack.
5)Remove the spray tower and spray arm assembly by unscrewing the bolt through its center.
6)Take out the filter immediately beneath the spray tower.
7)Disconnect the motor wires from the wiring harness,making a note of which wire connects to which terminal.
8)Disconnect the pump assembly and drain hose from the motor.
9)Remove the motor from the base of the dishwasher by unscrewing the four bolts holding it in place.
10)Repair or replace the motor and reinstall,taking care to reconnect the wires the same was as they were attached to the old motor.
11)Attach the pump and drain hose to the motor.
12)Replace the filter,spray tower and lower spray arm assembly.Reattach the center bolt in the spray tower.
13)Restore electrical power and turn on the water supply valve.
14)Run a test cycle to check for leaks underneath the appliance.
15)Replace the kick panel in front of the dishwasher.

If the spray tower is not in place then water will not get to the spray arm for the upper rack. You should be able to re-install the tower. Look for small tabs at the bottom that fit into slots in the mounting. The tabs should snap in or lock when the tower is turned slightly. If the tabs are broken off you should replace the tower. You can use the dishwasher without it but he dishes on the top rack will not get cleaned and the pressure tot he bottom spray arm may be reduced causing dishes to not get completely coean.

There have been many versions of the spray tower used over the years. If you have the model HDA3400G which you posted under, you should get a part number WD22X10008 which is the lower spray arm and tower assembly. By looking at the new part, you will see how a couple tabs hold the part on, and can figure out how to remove the old one with a flat blade screwdriver (or two). If you have a different model, please post the exact model number. The model number sticker is generally located on the left side wall of the tub, right by the front.

Yes, I was able to get it fixed.
The spray tower actually fits in the rack (I had thought it fit in the top of the lower spray arm - wrong!)

If you were to look at the spray tower itself, it has 2 little clip like plastic protrusions that with a little twist will clip onto the lower rack!

Push the lower rack in and you can see where the center would be, (right over the middle of the lower spray arm ).

Now pull out the rack and take the spray tower and slip it under the rack up thru the bottom in the position you noted was the center (from above).

Now with the spray tower in place, slide the rack back inside the dishwsher and you will see that the tower will be sitting directly over the top of the exact middle of the lower spray arm.

Voila!

I got the same problem and spent a couple of days trying to figure it out. The solution is extremely simple - you just snap the tower to the bottom tray. You need to lift the tray, insert the tower through the middle cell of the tray, and just snap it on it. That's it - no bolts, no connectors, nothing.

The Spray tower fits in the bottom rack, Its actually pretty obvious as there is no way it can sit int he position it has to without being in the rack itself otherwise the rack and tower would block each other all the time. 
 Examine the base of your spray tower it should have two "clips" or plastic protusions that will, with a circular twist, snap onto the bars of the middle of the rack itself. Then when in place and your rack is slid inside the dishwasher the tower should sit directly over top of the exact middle of your bottom spray arm. 
et Voila. 

Are you talking about the tower attached to the lower rack?