The title speaks to only half of the issue: the other half are the settings in Ubuntu and the sequences therein.
The computer in this issue does receive internet with the external antenna jack at the back being fed with a simple magnetic base antenna designed for putting on the roof of an automobile. However, that signal is weak and the Engenius with an external antenna (Rootenna ~15db gain) and ehternet wire will supply a stronger, faster signal. I've set the Engenius to the desired source and entered the correct WEP password. The lights on the Engenius indicate that it's connected to the access point.
At the Ubuntu side of this I've worked to no avail changing settings with "Edit Connections" to the point I'm Ask(ing)Ubuntu for help. I have and have RTFM for Engenius 3500
There is an embarrassing side note to this issue: At one time I had the Engenius working! It seems that I can't recall the settings and sequences I used way back when. And I may as well confess to not knowing the Command Line. I'm a GUI guy.