Someone has chmod 777 /etc on my virtual machine... can I repair without root?

So basically someone has run chmod 777 /etc which has knocked out ssh and sudo access.

I do have access via a non-root user. Any way I can at least run chmod 440 /etc/sudoers so I can at least get in and repair the damage. Don't have access to the console at the moment and tried messing with /etc/cron.d files but then noticed it's shutdown due to the permission problem too.

Any ideas?