** Kenmore washer model 110.27492600 fills with water and will not do anything else. Won't agitate, drain water or spin. **
The main motor is responsible for all those missing functions. It sounds like it isn't working... for whatever reason. That could be from the motor being defective, a bad timer or on your model, the lid switch (see the following link) isn't being activated or is defective.
On older washer models the lid switch would only stop the spin and drain functions but on yours it stops all motor operations. It might be a good place to start checking.