PassWare can enable Administrator accounts but it's not free. Also domain computers will cache previous logins when it was attached to the domain so you could call the client and ask them for the last users login credentials (along with advising them to reset the password in question immediately).

The second option only helps you if the user in question has administrative rights.

Even with these options, I'd still not recommend doing so as the computer and OS doesn't belong to you. Call the client and ask them for guidance, chances are the IT department (or whoever runs their IT) forgot (or wasn't informed) that you'd be off the domain.

For Git Bash

If you are running msysgit (I am assuming you are) and are looking to run Git Bash (I recommend it over TortoiseGit, but I lean to the CLI more than GUI now), you need to figure out what your home directory is for Git Bash by starting it then type pwd (On Windows 7, it will be something like C:\Users\phsr I think). While you're in Git Bash, you should mkdir .ssh.

After you have the home directory, and a .ssh folder under that, you want to open PuTTYgen and open the key (.ppk file) you have previously created. Once your key is open, you want to select Conversions -> Export OpenSSH key and save it to HOME\.ssh\id_rsa. After you have the key at that location, Git Bash will recognize the key and use it.

Note: Comments indicate that this doesn't work in all cases. You may need to copy the OpenSSH key to Program Files\Git\.ssh\id_rsa (or Program Files (x86)\Git\.ssh\id_rsa).

For TortoiseGit

When using TortoiseGit, you need to set the SSH key via pacey's directions. You need to do that for every repository you are using TortoiseGit with.