Thank you for the 2 great links. I took the drain valve apart one more time and decided that the rubber boot was not the problem. I restarted the machine and, when it got to the drain portions of the cycles, I got a loud buzzing and the solenoid seized up. I tried to check to make sure that I had put the wires back correctly but was confused when I compared it to the wiring diagrams published in the manuals. My machine's drain valve has a single prong at the top with a double connector - on the top is a yellow wire that goes to the pump motor. (In the manual, it's shown as a white wire.) Below that there are 2 white wires, one connects to the fill valve and the other connects to the fan motor. The lower prong has a pink (red) wire that connects to the timer above. The set-up is such that it would be impossible to reconnect the wires wrong.
I have absolutely no idea why the drain valve stopped working but it started to smoke a little and that was the end of it. Before that, I could manually open the drain to let water out but now it's seized and not functioning.
I will order the new drain valve and hope that that solves the problem. I should also probably have someone snake the drain. It's hard-piped and getting at it will be a nightmare. I doubt that it's ever been snaked in the 40+ years that it's been here. Any other ideas as to why it draining slowly? I sure hope it's not the timer.
Thanks, again for all your wisdom.