Ok well I've had it working for a week now and I should write up what I did. Connecting to the open networks took two hard resets. I also happened upon a very fine program called Wi-Fi Companion (
http://www.socketmobile.com/) that shows a lot of detail about wi-fi connections and also allows connecting from it. It also, in addition to Apache adjustments for "best performance" and battery life, can manage the radio itself optimally for power saving. Several have noted the Apache setting can make a difference.
I suppose I should uninstall Wi-Fi Companion for a true test but for now I'll leave well enough alone. I have no association whatever with this firm.
Anyway once I was able to talk to the open networks I still couldn't connect to my system, which was also open for this test. What to do?
Well I have a second DI-524 access point that was in a box in the basement. I did a reset of it, then hooked it to a desktop computer and nothing else. And I was able to connect with the Apache! Hmm. Now it was a simple and tedious process of comparing all the settings between the two. And I found it, eventually.
Somehow, when I originally set up the network three years ago I left the router set with the radio TX rate at 54 megs. As we should all know by now the Apache is only capable of 802.11b speeds, or 11 megs. So they would never connect. All I had to do was set the speed to "auto" and everything works!
Someone might put this info about access point speed in a guideline somewhere easier to find along with the already described info about using b or mix mode instead of g.
Thanks to all for reading and thinking about this annoyance.