I couldn't determine the problem for certain, so I called an appliance repair place that came out and told me it was the timer. The service call for diagnostic was $60, and they quoted me $350 for the part and repair, and said it would take a week to get the part. I paid the $60 and said thank you but no thank you.
I found the part here, for less than the price they quoted me for the part alone. I chose standard delivery, they shipped the same day, it was on my door step the next afternoon! After spending some time online watching repair videos (and FINALLY finding one that worked like mine) it took us less than 30 minutes from start to finish and it's fixed! THE NEXT DAY!
Here's how we did it. UNPLUG the washing machine first! Pulled the washer out from the wall to have room to get behind it, unscrewed the 3 screws at the top of the control panel cover, then unscrewed 2 hex nuts at the bottom of the panel cover. This is important: Unplug the plastic wiring harness and the ground wire FIRST. The ground wire is easy, the wiring harness is a little harder, just squeeze the plastic tabs and pull straight out. Then from the front of the machine, take off the selector knob and spring and cover. That will reveal the shaft of the timer and 2 screws that hold it in place. Unscrew them from the front, then remove the old timer from the back. It takes a little twisting and turning to get it out of the space around lid switch wires (didn't want to disturb anything we didn't have to) but it comes right out. Put the brand new OEM timer in, plug in the wiring harness and ground wire in the same place, line it up with the screw holes on the front and screw it into place, replace the selector cover plate, spring, and knob. Plug the machine back in, test the washer. Ours worked, so unplug washer again, put back control panel cover back on, move the washer back in place against the wall, plug it back in. REJOICE! Now go wash your clothes!
It was well worth the $60 to pay to know exactly what was wrong and what I needed to do to fix it, rather than try belts, agitator assembly, etc. Even including that charge, I still spent less than half what I would have to have it repaired. I saved over $200 and got to keep my old washer working!