This is a mystery to me because I have this printer installed in Hardy and I did
not have to do anything other than go to Add Printer and choose Brother DCP 7020
from the list. If anything my setup should be more complicated because it is a
network printer attached to a print server.

I suspect that things became broken as a result of some of the troubleshooting
before you came to us for help. There are no dependencies to resolve or install.
You don't need to download any debs or use Gdebi. This is where you get
problems. Anyone can upload a deb or a script to the internet. Not all debs are
the same. Making a deb is more complicated that it seems. They are made
specifically for a distribution and all of the dependencies need to be resolved
so that everything is from the same generation.

To get your printer to work, you need: CUPS, Foomatic and Gutenprint. All three
are in the repositories and work as I have used them to install many printers. I
now have four different printers in the house from four manufacturers (2 Laser
and 2 inkjet) and all work. In the past seven years I have never had a printer
that I could not get to work with Linux. This is better than my friend who had
to buy a new Laser printer when he upgraded to Vista because HP would not
provide Vista drivers. They would rather sell new printers than make drivers for
old ones to bilk people with more money than common sense.

You sound a little frazzled. I would go to Synaptic and remove completely (not
just remove) CUPS, Foomatic and Gutenprint. If you can remember the other things
that you installed from debs I would remove them as well. You can probably find
them in Synaptic by going to Custom Filters on the left hand menu at the bottom
and look for Package with Debconf or Origin and look for anything outside of the
usual repositories. Right click on the package name which will have a green box
and choose Mark for Complete Removal when you have them marked then click on
Apply. Afterwards, re-install CUPS, Foomatic and Gutenprint only and use nothing
but the repositories.

Once they are re-installed try to add the printer. Make sure your printer is on
and attached. If the exact model is not in the list (it should be because I use
that printer), choose a close one. Print a test page to be sure.

A word to the wise, never install outside of the repositories unless you know
what you are doing. It is a sure fire way to break your system so that you
cannot install or uninstall anything.