These all in one systems are specialized things really, like the imac and so forth - they are designed for a specific hardware set with set thermal, power, and noise restrictions, so you wont usually find a barebone version since they only hold a few types of parts.
But there are a few systems that might be the type of thing you are looking for. First is the barebone systems based around the intel atom such as the
Shuttle SD50X based on the Atom 330 or the newer
Shuttle X50V2 based on the D510. They are both barebone systems based around a 15.6" touch screen and you simply pick the ram and hard drive.
Another option would be to build your own mini itx system in something like the
Gigabyte SPIM51, and you can choose everything that goes inside along with what monitor you want to bolt to it - up to 23".
Beyond this your best bet is to search ebay or craigslist to find someone who had an all in one pc that broke, and you simply buy that off them. But given that most of those systems were using non standard parts more akin to what you find in a laptop than a desktop, you wont have a whole lot of options to fix it up beyond just buying the same parts that once sat in there.