More information:
commands in the git-bash shell work as expected
in the git-bash shell, Git\\bin\\git.exe is called>
Not definitive (it doesn't explain why git is working on one of my computers but not the other), but it does provide some insight into what might be going on: https://groups.google.com/forum/#!topic/msysgit/VrQLAgQwJHM
I have installed the portable version, added it to my path, and git is working as expected again.