Well I know this much, if you install and run a program called Piriform Speccy, that should help you narrow down your system specifications. Outside of that idea, I guess you can run a LiveCD of Ubuntu, install a program that does a similar thing and figure it out from there.
The annoying thing about pre-built computer is that they don't usually give you the exact details to the hardware that they put in them. At most they give you half the details, and if you are buying a computer based on too many details then you will most likely be a custom build computer builder anyway, who should just do it themselves.
What I am confused about is why you need to narrow down the specific OS when something like a fresh/clean retail copy of Windows XP to 7 should cover most (if not all) hardware configurations. What your computer probably is, is built by the manufacturer Hewlet Packard. I assume Pavilion is a computer range. And EMachines W2828 is the make/model, useful to narrowing it down on the manufacturer website.
I just did a search for W2828 on the HP website and found no results. This is not a computer model that they sell. Turns out it has something to do with this
. This isn't an operating system you can install. Apparently it is just to help top up all the drivers your computer needs based on the hardware installed. If you need to return your computer back to factory settings, you need to do it another way. You may have a disk or function you can use to activate a hidden partition on your hard drive and start the restore process, or a disk which you can use to reinstall your computer from.
Just to clarify, what are you trying to achieve here?