Be sure that you've used the "Credentials" link from the top of the Jenkins UI to add a new RSA private key for your user, and that you've confirmed separately from a git command line on that Windows machine that the credentials allow you access to the github repository. Use that credential in the repository section of the job definition.
You could check if "running as a service" is the problem by stopping the service you're currently running, and starting Jenkins on that machine with "java -jar jenkins.war". Define a job in that fresh running Jenkins, and see if it can read from that repository.
If that bug is the problem, you could enable the JGit implementation (using "Manage Jenkins" -> "Configure System" -> "Git" -> "Add Git") and try the JGit implementation from your Jenkins running as a Windows service.