I work at a computer repair shop and we have a lot of old AGP video cards laying around and I was wondering if it would be possible to turn them into single board computers. I mean you already have RAM and a processor, all you would have to add is a PSU and some sort of storage.

Graphics cards work on the bases of precision video Data ( polygon) rendering ( creating the polygon than texturing), the conversion process of turning a AGP card into a motherboard for a homemade computer is possible but you would have to script and engineer a operating system with dedication for such hardware. It IS possible but unless you are both a hardware engineer and a software engineer the process would be regretful in terms of performance. Most leaps in hardware engineering have been in graphics because of the mass COMSUMER need for things to " look pretty". Cpu's have a completely different layout in terms of a physical design; cache mainly. Every computing piece is made for such a reason and only that one reason ; modifying would require to re engineer the whole thing; in hindsight of your question... Before I went on a rant ; No; though I wish the same.

I am currently studying Computer Engineering, but am just about to start my second year. Haven't covered much hardware stuff yet. I know it would be entirely impractical, but I just thought it would be something interesting to try. Writing the OS would probably be the most time consuming, unless someone has already written one for the GPU I choose.