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" As I wrote in answer #2, there was an OS DVD that came with this eMachine and marked as such, it was indeed factory issue, not something created by the end user."
I'm a slow typist, and sometimes I have the page for a topic loaded for a while without refreshing it before I have finished typing and have submitted a response post.
I don't think response 2 was there in the un-refreshed thread when I had finished making what became response 3.
I have responded to probably at least a hundred topics about eMachines systems on this site and on another site, and a very common thing in those is the person said the eMachines system came without any Recovery disks.
That's the very first time I've ever heard of an eMachines system coming with any Recovery or Windows disk when it was new.
"....this was purchased by the client as a used system...."
You can buy Recovery disks for eMachines systems, from the eMachines web site, and/or from a small number of other web sites on the web. If it was a used system, how can you be sure the system originally came with it ? The original owner could have bought the eMachines Vista DVD from the eMachines web site or from one of those other web sites.
" I did notice that it was copyrighted to Gateway, which I suspect picked up eMachine at some point. "
Acer, eMachines, and Gateway are all companies of the Acer Group of companies. Acer bought out eMachines first, Gateway later, years ago. In some cases some of their models use the exact same mboards for more than one of their brands, although the mboard has a bios version specific to the brand.
"There apparently was some damage undetectable to the eye which caused the "missing files" message."
I have come across many Dell , Compaq, and HP systems that originally came with XP on them that came with either a Windows CD, or a Windows CD and at least one other disk that had drivers, sometimes programs, on it, when they were new. The Windows CD had brand name system labeling, not the Microsoft holograms and labeling. E.g." XP Home SP2 Re-installation CD" or similar, and when I compared the contents of the CD to the contents of an official Microsoft OEM CD for the same version with the same SP updates or no SP updates, all the files on the Windows CD supplied with the brand name system were identical to the ones on the OEM CD, with the exception that certain OEM files had been modified.
Is the Vista DVD an actual "factory" disk, or is it a "burned" disk ?
If it's a burned disk you can see where the data is on the disk.
Some brand name systems have a second partition on the original software installation on the original hard drive that has all the data that is necessary to install what was originally on the C partition. That's often called the Recovery partition.
Some brands hide that from you seeing it in the Windows installation; other brands allow you to see that it's there, but strongly discourage you from altering the data on it in Windows when you try to access it.
In either case, that second partition is shown in Disk Management in Windows, and when you boot the computer from the Windows CD or DVD and choose to see what partitions are on the drive.
Sometimes there is a program installed in Windows by the brand that allows you to make either a Recovery disk set, or a single Recovery CD or DVD for booting the computer from that allows you to use it along with the data on that second partition to restore the original contents of C; sometimes that's built into the bios version - you don't need a disk to run the Recovery procedure - you just select the Recovery option in the bios, or while booting the computer if a line pops up regarding that, or similar
Some brand name systems have a second partition on the original software installation that is for something else - it's too small to be a Recovery partition.