Another update...
My new USB sound card arrived earlier today. I have now a Diamond Xtreme Sound 7.1 USB sound card that I bought on Amazon. It has taken over for the two different PCI sound cards I've used. My USB headset was mostly a temporary fix as I've been unable to use features like Line-In and such for recording and doing other stuff. Also, I could use my original headphones again. I might have found my long-term fix for sound with this PC.
Aging PC and all, USB is working for me.