Generally speaking you need to set the display properly before you install. If
you had changed the display to vga from grub at the initial booting before it
was installed then you would not likely have had the problem. When the Live CD
boots, you can change the graphics settings with F4. This enables you to control
the way Ubuntu boots on its first boot up.

Once it is installed the settings are then stored in xorg.conf and it is
trickier to work with the file because if you mess it up then you may be working
in text mode until it is sorted out. Worse things can happen and you won't be
able to read the screen at all.

Puppy is generally set for lower resolution to begin with and Puppy Linux is
going to look the same on my computer as yours. It won't use my 3D graphics
card, etc. but will just give the plain vanilla to all. Ubuntu tries to get the
most of the graphics card and Ubuntu will look different on different computers
because of it.

What we need to do is to figure out how to get your computer to work at a lower
res and stay there. This is problematic on several levels. If we straighten it
out, it may become a problem in the future because your settings will change if
xorg, gdm, the kernel or your drivers are updated. There are no guarantees that
we can get it to stick.

Possible solutions include running an older version of Ubuntu or even another
distro, running a distro that is meant for older computers such as Puppy, DSL,
Minime, or AntiX, or persisting and being prepared to repeat the process once we
get a handle on it. You have been exceedingly patient thus far. I am not sure
how persistent you are willing to be.

I am not a graphics expert, and you may want to look further afield at a site
such as Linuxquestions.org or the forums specific to distro that is dedicated to
older computers. My experience is limited because my card tends to work without
much fuss. People who are likely to be able to help you are ones that have been
there and done that. I will of course add my 2 cents, but you seem to be running
out of suggestions on this forum, I think. I don't want to give you false hope
by pretending to know an easy solution.