Okay, installed the Realtek drivers, plugged a mic into the front jack, and it appears to work. The Microphone device on the Recording Devices pane goes to a green checkbox, and the stack-of-blue-rectangles gauge on the right shows activity when I tap the mic. I put that mic aside and moved the mic from the back jack and plugged it in there, too, and that one works on it as well, so its not a case of a faulty mic in the back.
On the other hand, I can't really see the back panel of my machine, the back of my machine is against a wall with too many other things in the way for me to get back there and look at it fully. I held a hand-mirror up to it yesterday, and could see the color of the jack the mic was plugged into, and it matched the color of the end of the plug, but I couldn't see the labeled name on it from that angle. However, when I plug the mic in there, it doesn't get noticed at all. There are a couple other jack ports back there I can find with my fingers directly under it in a line, but I can't tell what color these are either. On the other hand, the speakers are plugged into the jack immediately next to where the mic was plugged in at the back, and those have been working fine all along.
Any idea why the jack at the back isn't playing ball with me, and what I might do about it?