As far as I understand this, this is a problem with git on Windows. Shells work just fine with Emacs on Windows, it just can't supply the git password for some reason.
Except they don't. File-name completion replaced all backslashes with forward slashes, thus breaking cmd.exe's built-in commands. I reported a bug; it started a short discussion; i was asked whether I had to use cmd.exe (YES, I have reasons for why I MUST use it); nobody really acknowledged it was a bug; the discussion died off in talk about some internal details. (The 24.4 binary package is not yet available for windows so I couldn't test it.)
I actually had a similar problem in the past. My workaround was to use some utilities from gnuwin32, which are native windows ports of the gnu utilities. With that, you can use gnu mkdir, rm, ls etc instead of the cmd builtins.
