I finally managed to get Anaconda to start working by executing the line:
pip install pywin32==300
I had to do it twice, because the first time it went for 301, not 300. The second time then dropped it to 300. This was from the Anaconda for Windows installer downloaded just two days ago from the Anaconda website and doing a "clean install"!
What a fiasco!
Until that point, NOTHING really worked. Almost every important command within Anaconda would fail with the Win32com error, and Navigator would not even start. Apparently the latest version of pywin32 is 304, but it doesn't work either. Is anyone looking into this? For a newbie like me, this is a very bad look for Anaconda as a tool! I was on the brink of simply giving up when I literally stumbled onto this thread.
Note that it has been MONTHS between my post and the one before mine. I'd say that this has probably caused a lot of people to simply give up (assuming that there are many who actually try to install this on Windows per month, that is).