Win7 error: "CLR initialization failed with error 800700c1."

Solution 1:

I finally got it fixed.

As I suspected, it was related to a (possibly) corrupt 64-bit DLL MSVCR80.DLL.

I uninstalled all the "Microsoft Visual C++ 2005 Redistributable" packages (both 32 and 64 bit) via the regular uninstall screen from the Control Panel - I had 3 such packages.
After this, everything returned to working order.