I believe it's the OpenAL32.dll's dependency on ole32.dll, which has this odd list of dependencies:
- API-MS-Win-Core-Debug-L1-1-0.dll
- API-MS-Win-Core-ErrorHandling-L1-1-0.dll
- API-MS-Win-Core-Fibers-L1-1-0.dll
- API-MS-Win-Core-File-L1-1-0.dll
- API-MS-Win-Core-Handle-L1-1-0.dll
- API-MS-Win-Core-Heap-L1-1-0.dll
- API-MS-Win-Core-Interlocked-L1-1-0.dll
- API-MS-Win-Core-IO-L1-1-0.dll
- API-MS-Win-Core-LibraryLoader-L1-1-0.dll
- API-MS-Win-Core-Localization-L1-1-0.dll
- API-MS-Win-Core-LocalRegistry-L1-1-0.dll
- API-MS-Win-Core-Memory-L1-1-0.dll
- API-MS-Win-Core-Misc-L1-1-0.dll
- API-MS-Win-Core-ProcessEnvironment-L1-1-0.dll
- API-MS-Win-Core-ProcessThreads-L1-1-0.dll
- API-MS-Win-Core-Profile-L1-1-0.dll
- API-MS-Win-Core-String-L1-1-0.dll
- API-MS-Win-Core-Synch-L1-1-0.dll
- API-MS-Win-Core-SysInfo-L1-1-0.dll
- API-MS-Win-Core-Util-L1-1-0.dll
- API-MS-Win-Security-Base-L1-1-0.dll
Likewise, OpenGL32.dll requires ADVAPI32.dll, which as a similar list of dependencies.
I'm not sure how these misconfigured DLLs got on my system, but all those API-MS-*.dlls are Windows 8 stuff.
http://msdn.microsoft.com/en-us/library/windows/desktop/hh802935(v=vs.85).aspx
(I'll have to figure out how to fix either the affected DLLs or install the Win8 API set.)
Alas.
[edit] I found them. They're in the Side-by-Side system directories...
Now to check to see if they're really working right...
[edit 2] So that's not the problem...