I did a registry access trace using SysInternals' Regmon, both on the
computer that didn't work, and on the one that does.
In order to fix this, I had to import the following registry key:
Windows Registry Editor Version 5.00
[HKEY_CLASSES_ROOT\CLSID\{4c892621-6757-4fe0-ad8c-a6301be7fba2}]
@="Windows Settings Page"
[HKEY_CLASSES_ROOT\CLSID\{4c892621-6757-4fe0-ad8c-a6301be7fba2}\DefaultIcon]
@=hex(2):25,00,53,00,79,00,73,00,74,00,65,00,6d,00,52,00,6f,00,6f,00,74,00,25,\
00,5c,00,73,00,79,00,73,00,74,00,65,00,6d,00,33,00,32,00,5c,00,74,00,68,00,\
65,00,6d,00,65,00,75,00,69,00,2e,00,64,00,6c,00,6c,00,2c,00,37,00,00,00
[HKEY_CLASSES_ROOT\CLSID\{4c892621-6757-4fe0-ad8c-a6301be7fba2}\InProcServer32]
@=hex(2):25,00,53,00,79,00,73,00,74,00,65,00,6d,00,52,00,6f,00,6f,00,74,00,25,\
00,5c,00,73,00,79,00,73,00,74,00,65,00,6d,00,33,00,32,00,5c,00,74,00,68,00,\
65,00,6d,00,65,00,75,00,69,00,2e,00,64,00,6c,00,6c,00,00,00
"ThreadingModel"="Apartment"