I finally found the solution (for me). It's apparently related to certain motherboards, one of which my Alienware uses.
The problem is caused by the system file ndisrfl.sys (C:\WINDOWS\system32\drivers\ndisrfl.sys). This file is used by a program known as "Intel(R) Technology Access Filter Drive". More information about this program is provided here:
https://communities.intel.com/thread/83226
The gist of that article is that this program doesn't seem to have any use (that I could find) on a computer without a touch screen.
Uninstalling "Intel(R) Technology Access Filter Drive" fixed the problem on my machine, and I haven't noticed anything that seems to need it.
Before you uninstall this program, it's recommended that you create a restore point, so that you can go back if there are problems.