Windows 7 Pro, 16 gb ram, 3600 amd cpu
That system shouldn't have any problems. Are you sure you tried 0.87.2? The only place you can even get version 0.76 (github) does not have the latest version. Also, I recommend doing a full uninstall and maybe even remove the C:\Program Files (x86)\Armory directory, before reinstalling the latest.
Also, please try it in offline mode, too. There's a launcher in the start menu for it. It is extremely useful to know whether it works in offline mode, and you can easily get me a log file.
Thanks for being patient!