Kenmore 110 series top loading washing machine -- won't spin

[c71mac]

Hi all,

Here's the trouble.  5 yr old machine will not spin (or needs a good push) after it agitates.  Enters all cycles no problem -- fills with water, drains, agitates -- but when the spin cycle is up, nothing happens....motor is running and sounds like it is spinning.  I depress the control knob to stop cycle, hear an audible clunk, then pull it back out to engage the cycle again and it will begin to spin, but very slowly -- needs a good push to get it going, but once it starts spinning it is OK.  Had an appliance guy come out, he said it was the transmission (said it was leaking oil) and told me it wasn't worth it for him to fix it for me -- too expensive a job.  Recommended I buy the same model and use old one for parts when needed.  My question is does this sound like a transmission trouble, and , is it something I could do myself to get it working again??

Just got an Amana that was free in the meantime -- but had to replace the pump, the belt, and the hose -- only about 5 yrs old as well.