you installed Vista from a Microsoft disk (NOT an eMachines disk), then the Recovery Partition is GONE!
That's something only a factory disk would keep. Windoze will completely erase everything on the hard drive and then set the drive up to suit itself. I could be wrong here, but I have a sinking feeling that I'm not.
For that matter, over the years I've done Factory Restores on at least a dozen eMachines models, and every one I've seen yet will install from the factory CD or DVD to a blank hard drive. The later ones I've used will make a Restore Partition first, and then finish the job from there.