Probably the limits of the hardware--your video card may need to be
upgraded if you want the higher resolutions.

My two cents:

1) Ardell does have a point - but I'm using now-modest 2006 hardware
with Ubuntu Studio in Full HD (1920*1080).
I think that I even had it run in Full HD using the integrated video
card, before I happened to acquire a second-hand then-good separate
one.

2) I'm repeatedly experiencing a fall-back from 1920*1080 to 1280*768
with my 2009 powerhouse (running Windows).
It takes some shifting from one connector to another and similar
"no-ops" to have it eventually re-recognize the Full HD.

You may need to edit your xorg.conf file, as root. It is located
in/etc/X11, and that is a capital X. The important things to get right are
the maximum resolution and the horizontal and vertical frequencies.
Vertical is in Hz and the horizontal in kHz. You will have to look up the
number ranges (each has a maximum and a minimum) in the manual or online.

It might help to know what video adapter is in the computer. Open Terminal and
enter the command: lspci

One of the lines will include "VGA," perhaps you could copy and paste it here?

The report says:
VGA compatible controler: ATI Technologies Inc Device 9710

Took a look at the other suggested file to tweak and didn't find anything like
was suggested. At this point I'm going to just figure that the on-board video is
doing the best it can and if I want anything in higher rez I'll have to add
another dedicated video card. Not that big of a priority at this time. I'd be
better off spending my energy building a new OS system with a later version of
Ubuntu.

I just realized that 100% of the suggestions I might make, won't work due to the
version of Ubuntu you are using.

Another question is what kind of graphics card/chip set are you using
and are you using the open source or proprietary drivers for it? I get
moderately better definition from my monitor using the NVidia driver as
opposed to the supplied open source driver. They both do well at
resolution and refresh detection. I am using 12.04. If I remember
correctly, the 9.x series open source drivers lagged behind the
proprietary drivers. Might be worth considering an upgrade. Although I
would try a 12.04 live disk of your flavor to see if there is a
difference in resolution detection and display.