Hi. I think you need to resolve your Nero burning problem before we try to decide what to back up, because you will probably need a fairly large capacity backup medium. Can you tell us more about what you do to burn a disk with Nero. Do you have InCD with your Nero software because this could make your backing up easier.
Unless you keep all your files in a common folder such as "My Documents" you will need to identify what files you want to save. E.g. are they all Word files?
The easiest way to save your emails is to locate all files with a .dbx extension and save them all to a folder that you create for the purpose. Dont forget to make a note of all your internet settings. But first try to resolve your Nero problem, or get another hard drive to back up to.