What OS are you running? Can we get your system specs?
If you are running Vista or Windows 7, you should try running the game as administrator (right-click the shorcut, go to properties, check the box "run as administrator) or trying using some of the compatibility modes (right-click shortcut, properties, compatibility tab).
You can also try installing to a location OTHER than Program FIles, as this folder sometimes causes problems with older games. To change the install path, click the "options" button from the GOG installer.
One last thing you can try is the unofficial patch... I've never used it but maybe it will help. Check these forums for where to get it.