Fills with water then hums when supposed to agitate but spins and drains

That's an easy problem to fix. I will supply the manuals you will need to diagnose the problem. You will need to buy a digital multimeter at Home Depot, Lowe's, or Radio Shack. Here are the manuals: https://dl.dropboxusercontent.com/u/8010163/Understanding%20automatic%20washer.pdf
https://dl.dropboxusercontent.com/u/8010163/Whirlpool-Kenmore%20washers.zip
https://dl.dropboxusercontent.com/u/8010163/How%20to%20use%20Test%20Equipment%20Service%20Manu al.pdf

Most likely you have a problem with the "Agitate and Spin Solenoid" that will require testing with your digital multimeter (DMM).