So looking around I noticed my normal network adapters behaving strangely. I did a "reset network settings", and it removed the drivers on the adapters - no problem, I backed them all up beforehand. What was weird, though, was that windows would not let me install or update the adapters because of "Code 56":

At this point I concluded that there was something very wrong, so I went for a full system reset. After that, I reinstalled VMware, and it worked! The installation went smoothly, didn't hang or crash when installing the drivers, and when it was finished the virtual adapters it installed worked!

So yes, RaSystemlord totally called it. It was definitely something snarled up besides the installer!