No, I did not mean the resin tank when I used the term "cylinder". I was referring to the housing that the piston assembly fits into. At the bottom, underneath the piston assembly, is where I found these pieces.
The valve is working fine now...
I think I just answered my own question...
A couple of weeks ago, I had a problem with my well pump. I pulled the pump and discovered that the check valve, which is integral with the pump head, had broken. Here is a pic of the check valve....