Washer works on only 1 setting

Assuming that you've installed the stack kit according to instructions, you should check the following:
1. The dryer should be securely attached to the washer and not wiggle or move. The washer must always go on the bottom of the stack.
2. Washer should be level and have all four level legs making solid contact with the floor, no wobbling.
3. Make sure the drain hose is not pinched or restricted (or there is not debris in the drain pump) as a slow pump out will accentuate vibration problems.
4. Make certain you've removed all of the washer packing bolts before using the machine (see owners manual for description.)
5. The floor must be solid with no "springy" or "spongy" feel. No matter what you do to the laundry set it will vibrate on a less than solid floor. This occurs on upstairs installations or other wooden floors, especially in an older home. Sometime the floor can be braced to stiffen it. Also, vibration pads are sold that might help minimize the vibration. The walking is a symptom of vibration.

Experience shows that most problems of this sort result from incorrect installation and/or flooring issues, not the laundry. You should not attach it to the wall. It is possible the washer has a problem in which case a technician would need to check the unit. They can check the suspension and drive system for proper operation.

the controller of that unit may get carotted

Sometimes there is a GFI or ground fault interrupter switch in the circuit. This is a wall plate which has a mini switch between both plug-in holes in the wall plate. Sometimes these are wired in-line where you have 1 master and additional outlets. This means that if the wall plate your washer and dryer are plugged into does not have a little red or black button to push to reset, there may be another wall plate in that room which has it instead.

Sometimes circuit breakers in a fuse panel are marked wrong. You may need to reset a different breaker.

No the Kenmore 98702 Stacked Washer / Dryer has only 1 power source just the 220V
Installation manual is located Here

hi gar.... sounds like your dryer vent pipe or outdoor vent is partially clogged with debris. thoroughly clean it out and it will work great once again. Joe

first of all. comming from a Sears Technician.. (don't yell) -- the delivery drivers only know about delivering stuff. they dont know too much,
if the two are the same size they can be stacked.
sometimes have to rig something up
and yes, for that model the top is removed, clips go on the rear and screwed at the front.
in some areas it is sold seperatly as a stacking kit

Are you connected to a 30 amp breaker w/ 30 amp wire?

My twin stacking whirlpool washer/dry. The timer switch kicks on but does not dry clothes kicks off after 5 mins but, clothes still wet.

Hi..I had the same problem yesterday...the maching would start when I pushed the button and then stop..I had to push the button again to get it going..My stacked set is around 8 years old.

Here's what we did..moved the washer away from the water source and unscrewed the water intake lines..there is a little screen there...took the screen out of both hot and cold lines..one screen has some debris in it..the other was almost completely blocked..we are on a well and sometimes dirt..etc..gets in the lines..

Today no problems doing the laundry..its working like new..

couple things this could be lets start obvious
faulty door switch even though door latches doesnt mean its working properly
bad guages easy to check dont have to run dryer just guages
turn on setting let run threw cycle if it stops on cycle and dont move for a length of time this will be the problem

these 2 things are main causes of why a machine wont work or partcially works at times everything else is easy