@Whiskeyover
Are you running the setup through the autorun? Because that usually doesn't work right. You need to close the autorun, open the setup program's properties, set the compatibility mode there (I think WinXP SP3 works best, though if not you can try all options all the way back until Win98), and then launch the installer exe directly.
If that doesn't help, it might be the DRM thing. See, unfortunately, Microsoft decommissioned the DRM system used by the game (Safedisc/SecuRom). I'm not sure if the setup already checks this, but if so, this might be what causes the issue. And even if it isn't, you won't be able to run the game correctly unless you look into that.
More info on this can be found here:
http://www.howtogeek.com/230773/how-to-play-pc-games-that-require-safedisc-or-securom-drm-on-windows-10-8.1-8-7-and-vista/
The issue has been discussed in detail in this thread here on the forum:
http://answers.ea.com/t5/C-C-The-Ultimate-Collection/Command-and-Conquer-Generals-Zero-Hour-Windows-10/td-p/4701341
The posts by the user PADYWAN1 have some really good research.
The easiest solution for this, as long as you're not on windows 10, is to find and uninstall the Windows update with name KB3086255. This is the one disabling the DRM system. You'll have to temporarily disable automatic Windows updates to make sure it doesn't automatically get reinstalled, though.