Does it work if you disable your firewalls? (Unplug from internet; disable firewalls; reboot both.)
I wasn't knowingly running firewalls since I use Kaspersky Internet Security on both machines (and recommend it highly!). However, Windows Firewall had appeared again on the Dell; I usually have that disabled. I disabled it again and rebooted. After this, the icon in My Network Places disappeared, although I am still able to get to my workgroup through the link to view the entire network; however, it still gives me the "inaccessible" message.
I will try disabling KIS when offline, reboot, and see what happens.
In the meantime, too, I've realized that I had overlooked what Soybean said about Internet Connection Sharing. My main purpose in this adventure is to enable the Dell to use the air card that is in the HP, as well as to use the files and applications on the HP via the Dell's screen. The HP was set up to be the residential gateway and the Dell to connect through the HP to the Net, but now I have also enabled the HP's connection to be used by all computers on the network (just the Dell in this one). It hasn't worked, but there seems to be quite a lot to Internet Connection Sharing and I have to go through all the Help documentation on it more thoroughly.
Sincere thanks for the helpful suggestions, and I will check back with results soon.
Barb