jonsamava Your C drive is somewhat low on free space. While 16 GB free isn't so low that it would prevent Sims 3 from working (at least not by itself), it's still low enough to possibly present some system issues now or later. So please try to free up at least another 10 GB.
If you've installed any mods at all, please move the Mods folder to the desktop. A mismatched core mod will typically cause the game to minimize or throw an error at the Main Menu, not a black screen, although it's certainly possible for any mod to do this. You mentioned that you removed mods, but does that mean you removed all of them, or just some? If you haven't already, please remove the entire Mods folder.
If that doesn't help, please remove or rename the entire Sims 3 folder in Documents > Electronic Arts so the game generates a new one. This will remove, but not delete, your saves and other user content.