I have Unity 2.6.1, Blender 2.49b and Python 2.6 installed on Windows 7. I get the following error for all .blend files: Blender could not convert the .blend file to FBX file. You need to use Blender 2.45 or higher for direct Blender import to work.
I set Blender to run in admin mode, otherwise you can’t run the python scripts, but that didn’t help the Unity problem.
Works here, I’ve also got Unity 2.6.1, Blender 2.49b and Windows 7 (64bit Home). The FBX exporter is native to Blender so you don’t need a full install of Python, although that shouldn’t effect it. What happens of you double click on a .blend file from Windows Explorer? If it doesn’t launch Blender automatically, then you may need to set Blender as the default app to open a .blend.