I've tried to install Zeus on my laptop, but whenever I open the game the screen goes black, the resolution changes a few times, and then the game crashes. I've tried all the compatibility options, changing my laptop's resolution, deleting the binks folder, reinstalling the game, and installing the widescreen fix - none of it seems to work. My laptop's graphics are Intel HD 5300. The game works fine on my desktop. Does anyone know of any other solutions, and is there a debug log of some kind where I can see exactly what the problem is?

There are no debug logs for the game. Have you made sure to check you have no overlays running, like nVidia Shadowplay? These have negative effects on the game and should not be running when playing the game.

I have the exact same problem, like I mentioned in Cleopatra forums

https://www.gog.com/forum/pharaoh_cleopatra/game_crashes_on_startup_goes_black_screen_back_to_desktop_and_has_stopped_working_message

I have the same issue,

I also run it on a potato netbook with an Intel Celeron N3050 an Intel HD Graphics.

I start the game, it switches around resolutions and then I get the "It stopped working" message.