The first thing you should do is smack both the guy that "uninstalled" the JDK and your entire sysadmin team. The first guy because he apparently doesn't know how to install and uninstall programs, the sysadmin team because apparently they have given access with installation rights to one of your servers to someone who shouldn't be able to install programs on it.
After that you should remove the uninstall information from the registry; it's located at HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\CurrentVersion\Uninstall. Go through the entries until you find one with the right display name, then delete the entire key. Then install the JDK again.