My operating system uses Windows 7 Ultimate, and it works fine with Diablo and the remastered GOG version. Everytime I launch Hellfire, it just crashes the program and gives me the "Hellfire has stopped working" message.

I tried searching in this forum for someone with the same related issue. It doesn't look like anyone else has this problem, unless I didn't look hard enough. Any suggestions?

Contact GOG Support. If this is a problem with Hellfire generally (such as if the installer failed to set some compatibility flag), they need to know about it so that they can fix the installer. If this is a problem with your system in particular, they may be able to help you identify what to change. They will likely want you to provide more information and/or change various system settings. They may not respond until business hours Monday.