My washer will fill with water, drain, and spin. It will not agitate. We have taken the agitater off, but what do I do now? How can I tell what is broken and what I need to replace? Any guidance would be appreciated.

I know it is spinning. When the spin cycle starts and I open the lid, I see the drum spinning (before it stops because I opened the lid).

I took that part out and it appears to be fine. It sits over the large metal piece and it will go back and forth. The metal piece it sits on will not budge. Is that part of the transmission? If so, is that expensive? I ask because the machine is just under 10 years old and if this will be expensive I will look into buying a new one. If I need to call the repairman it will get expensive in a hurry.