We have a kenmore washer 70 series model #110-20702991 that will not spin or agitate,
I have read may be the motor coupler?

It could be. Kenmore also had an unusal timer problem as well. Do you here motor running or humming?

Yes, the motor does seem to be running and it fills and drains fine.

Either the coupling is bad or the transmission is locked up. My experience is the coupling is probably bad. To check you only need to remove the motor. Not too bad a job if your handy.