Sounds like a Firefox/Windows issue. When you run Firefox it will attempt to load a profile. When you run Firefox manually it will look for your profile in your home directory, i.e. C:\Users\<login>\AppData\... but when you open an instance for FirefoxDriver I think it attempts to generate a temporary profile and opens Firefox using the temporary profile. If the directory Firefox is attempting to use has corrupted or bad permissions, it might not be able to launch Firefox.
I would put on my Windows-hat and start making sure my operating system is working properly. If you are not an administrator on your computer that could make fixing this.
You might also try finding Firefox resources which can help you with this. Bottom line, I don't think this is a common problem and might be unique to your environment.