Well instead of just cramming everything into a single zip/rar/7zip/... file, you can compress the stuff across multiple smaller compressed file types, and then burning said files to DVD/CD if available. Otherwise, seen as you now have multiple smaller files, you can upload these files to a free file sharing/storage site, can't think of one at this time.
There is also Microsoft's free SkyDrive account, go and get your friend a free Live account, then look for SkyDrive, upload the files, restore, enjoy.
You could also take the computer to a repair shop and get a professional backup performed, but seen as the files are so small, and I don't think the benefits will outweigh the cost.
There are many more routes you can take, so if none of these work, Google can surely help you out.