I first read the possible problem descriptions in https://www.appliancepartspros.com.
I then removed the parts to confirm. The cap was stuck but still removable. Good idea to put just a touch of grease when putting it back. As described as the most likely issue, the "agitator dogs" were worn.
The website gives the option to purchase only the dogs, but given that the other plastic parts were so old and must have been worn at the same time, I've decided to purchase a complete repair kit. Problem: I could not find the appliance model number on the clothes washer... Which one of the 3 repair kits do I need? Short, medium, or long??? I wish the description would include the length. From the pictures, the only part that looked different is the white/translucent cam. Solution: a small size, the faint number is visible on the old cam. This number was listed only in one of the "Cross Reference Information" descriptions: the Medium Kit. That is what I ordered. Purchased the normal delivery. Received it early on the second day. It took less than 10 minutes to install. This repair was really an easy one, thanks to the video and good information provided by AppliancePartsPros.com.