Short Version: I got Port Royale to work on Windows 7 by using the game's 1024x768 resolution.

Long Version: After being unable to find an online version of the original Port Royale with its lovely multi-ship naval battles, I was happy to find it at GoG. Even though the GoG entry says Port Royale is not compatible with Windows 7, I decided to but and try my luck regardless, especially because of the half-off sale. I also was able to run the Steam version of Port Royale 2 just fine.

After installing, I found Port Royale would crash after the load screen. I checked around online for fixes, including this forum, and didn't find any that worked. I tried running the program as administrator, in windowed modes, and under different compatibility (XP, etc) settings to no effect. After some attempts on different settings to play the Port Royale, I found that when the game's resolution is set to 1024x768 (in the game menu) the game doesn't crash after loading. I've been playing for around an hour so far and haven't crashed. *crosses fingers*

Since I didn't see this possible fix noted anywhere, I hope this works for other people!