If the game crashes on startup for you, try this fix.

Step 1
Right-click on the desktop and click Screen Resolution to see your active resolution.

Step 2
Go to Control Panel > Appearance and Personalization > Folder Options > View
After that go to Advanced Settings and select Show hidden files, folders, and drivers and then press OK.

Step 3
Go to C:\Users\YourName\AppData\Roaming\LucasArts\The Secret of Monkey Island Special Edition
Open the Settings.ini file in Microsoft Notepad and change the resolution to your active resolution.

For example:
resolution=1680x1050
resolution=1920x1080

Step 4
Save the document and start the game. If the crash was caused by wrong resolution settings it should work now.