man this is so lame Im reading posts that are 4 years old with my exact problem and no solution. although my copy does run except the screen is way too zoomed in and I can find no solution to fix shy of playing in tiny window mode. If anyone ever reads these I could use help or even a fucking refund since this is supremely irksome.
You didn't mention which problem you are having. Regardless, it can probably be resolved by using Exult to run the game (like one of the other posts mentions).
Go here: http://exult.sourceforge.net/download.php
Download the Windows binary snapshot, install it and point it at the Ultima 7 files under C:\GOG Games\....
Then run Exult and enjoy the game.
I played through the entire game using Exult about a year ago and ran into zero bugs.