Starting with a fresh trinity maverick install, I performed a release upgrade to natty.  I was then directed to http://trinitydesktop.org/installation.php for instructions on adding new lines to sources.list for upgrading my system to trinity 3.5.13.  These lines were added and "apt-get update" was performed.

The first issue encountered when performing an "apt-get upgrade" is that there are 865 conflicts detected.  After working at it for over 8 hours, apt was still unable to finish creating a list of possible conflict resolutions and was stopped.

To try manually resolving this problem, I first installed kubuntu-desktop-trinity.  This completed with the following:

> Errors were encountered while processing:
>  kubuntu-desktop-trinity
>  kdebase-trinity
>  kdebase-runtime-data-common-trinity

I had to run the following two commands, then I was able to install the packages without error:

# dpkg-divert --remove /usr/bin/plasma-desktop
# dpkg-divert --remove /usr/bin/plasma

I then manually installed kubuntu-default-settings-trinity, which completed without errors.  Rebooting my system at this time and attempting to start kdm-trinity presented the following error in kdm.log:

> kwin: symbol lookup error: /opt/trinity/lib/libkdeinit_kwin.so: undefined symbol: _Z14set_tqt_x_timem
> /opt/trinity/bin/kdm_greet: symbol lookup error: /opt/trinity/bin/kdm_greet: undefined symbol: _ZN7QObject18childrenListObjectEv

I was still unable to run "apt-get upgrade" at this point due to the large number of conflicts.  Believing these conflicts may be due to the kde3 packages still installed, I started removing them.  I used the following to remove packages, 50 at a time, because apt was not able to handle the entire package list in a single round:

# aptitude search kde3 | grep ^i | grep -m50 Transitional | awk '{print $2}' | xargs aptitude -y remove

One package remained due to the long filename being cut off, and I removed it:
# apt-get -r kdemultimedia-kfile-plugins-kde3

With the old packages out of the way, I was now able to run "apt-get upgrade" successfully, and kdm-trinity started without the previous kwin error.  To complete the upgrade, I went to my home folder and moved the kde3 folder to triniry:

# mv .kde3 .trinity

This completed the upgrade process, and I am now able to log into my original desktop setup under the new trinity 3.5.13 environment.