Even though somecoolguy's account in Github is private, you have an entire copy of the git repository in the server (Your branch is up to date with 'origin/master'). You should be able to create a new repository in Github under your account and add it as another remote
where you can push the git history.
git remote add anotherorigin [email protected]:myaccount/somecoolproject.git
Notice that this remote is pointing to your account instead of somecoolguy's.
If you don't want to play around with SSH keys (as the keys in the server probably belong to somecoolguy), you can link the new origin using https which will require your Github credentials when pushing:
git remote add anotherorigin https://github.com/myaccount/somecoolproject.git
Once you do that, it should be enough to push your repository to the new remote server. If you don't want to lose the changes that have not been committed yet, you can always commit the uncommitted files before pushing:
git add .
git commit -m "New commit"
git push anotherorigin master
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