Does the installer say anything about why it failed?
And yes, manually downloading those VPs is absolutely necessary (assuming we can't get the installer to work), without them, BP will not work at all.
OpenGL Vendor : Intel
OpenGL Renderer : Intel(R) HD Graphics 4400
OpenGL Version : 4.3.0 - Build 10.18.15.4256
This might be a problem. If this is the only GPU in the system, you should definitely disable things like Shadows and delete the bpc-advanced vp files, as the game will likely be unplayable with them. If you do have a dedicated GPU somewhere in there, you should use the driver's control panel to tell it to switch to that GPU when FSO is running.