I installed the 64 bit net client profile linked above, after which Cyberduck ran successfully. Windows update then prompted to install "Security Update for .NET Framework 4 on Windows XP, Windows Server 2003, Windows Vista, Windows 7, Windows Server 2008, Windows Server 2008 R2 for x64-based Systems (KB2160841)"
This installed succesfully, restarted my machine, and Cyberduck continued to work properly.
Guess there was some sort of damage to my .NET 4.0 install? Not sure what other .Net 4.0 programs I'm using, but I hadn't seen that error message elsewhere.