My Kenmore front-loader fills but does not tumble or spin at all?

My washer, model 26 40042, is nearly six years old. It fills but the drum doesn't move at all. I hear sounds after water enters the machine, so it thinks it is working, but nothing happens on any of the three cycles. It drains partly after the cycle has timed out but does not spin the water out fully. Before this happened, from time to time the washer would leave clothes very wet, so I'd give it another chance by turning the dial to a final spin setting and it would spin the clothes better.

I've turned the drum and it feels the same as before, so I believe the belts are in place. I've checked the latch, tried to clear the hose of any obstruction, tried running it empty, tried running it with a good amount of clothes in it, and so far have not been able to determine what is wrong.

We've already replaced the pump once--the other pump was ruined when something small got inside and ruined the gears. This machine has also had a recurring leak that I've fixed several times, which may not even be related to this current issue.

How can I determine which part is bad? Can I fix this myself, and is it easy? I'll call a repair person if needed but hope I can easily fix this myself. Thanks for any guidance.