I applied the Ultima II patch found in the Resource Collection in the forum. Everyting semed to patch correctly except that I stil have the old CGA graphics. It has not been updated to the EGA graphics. Does anyone know what might have gone wrong?

Go to the game's installation folder, where you've put the patch files in.
Run RENGAL.BAT
Then run u2cfg.exe
Choose "3" Save & Quit.
There should be a file named U2.CFG in your folder now.
Start the game with ULTIMA2.COM

I have successfully done all the steps up to the last one in your list, and verified that there is a file called u2cfg, as well as verifying that I have modified the save options to only save when I press Q. However, there is no file in my folder called ULTIMA2.COM. I have been starting the program with a shortcut provided in the original GOG version.

The mystery has been solved. The shortcut supplied with the GOG package calls up a file called dosboxULTIMA2_single.conf, which is sort of a script that runs the unpatched version of the game. When I changed the name of the file dosboxULTIMA2_single.conf runs to ULTIMA2.COM, it ran the patched version and everything seems to be working correctly, including the EGA graphics. It also has slowed the game down quite a bit, which makes flying the airplane less hair-raising.