Maytag Dependable Care Washer Model#LAT9314AAE.
Washer will fill with water, but will not do anything else.
We already replaced the timer, and the lid switch seems to be working properly.
Any suggestions??

Do you hear any noises like the motor running or other noises after it fills?

Thanks Doug. No. We don't hear anything at all. The timer will advance (click) through it's stages, but the washer doesn't do anything. No buzzing, no humming, no smoke, no funny smells... nothing. We tried adjusting the lid switch, but that did not help. Is there a way to bypass the lid switch? Or maybe an easy way to check what the problem is?

Yes, you can jumper around the switch. I would next check for power at the motor. Do you have a voltmeter and know how to use it? YOu should have an electrical diagram inside the console that will show you how the power runs to the electrical components.