So I upgraded to 4.3.2, and lately, I’ve been having a lot of trouble just getting it to run. It starts and I see the usual loading image, but then it fades and nothing else happens. I’ve checked my task manager, and the process just keeps running, doing absolutely nothing. However, it seemed to work when I first installed this version.
Right now, I’m trying a reinstall to see if that helps.
I’m not a troubleshooting expert in any sense, and I know this is probably the most annoying possible response, but did you restart the computer after (re)installing? Sorry, but this is the default reply for a reason 
Also, it would probably help to say how did you upgrade. For example, you upgraded from Unity 3x by uninstalling 3x and then installing 4.3.2 (which is unlikely, but just an example)
Is it attempting to load in and/or upgrade an existing project? If so, what happens if you start a new project? To do that, after clicking the icon to start Unity, immediately hold down the Alt key. That will 1) not open any previous project and 2) open a wizard that will allow you to start a new project. Does starting it that way work?
If not, you might try starting the editor in open gl mode (instead of DirectX - which is the default).
To do that, you need to add the “-force-opengl” command line switch when starting the editor. Does that change things?
If not, you might look at the logs it generates for clues. On Windows , that’s “%localappdata%\unity\editor\editor.log”.
Jeff
@jgodfrey: It worked! I remember trying to reopen a project from version 4.2.1, and it must’ve been acting up ever since! Thanks, though now I guess I’ll have to look at that project some other way… But that’s a small problem for me. Thanks again!