I'm unaware of a single site that can tell you all that info for all manufacturers, perhaps someone else can chime in. Please note, you won't always be able to find an FCC number, so the govt FCC lookup site may be of no use.
A quick look at the Motherboard MIGHT tell you what you need to know. If no PCIe and Sata connectors, you're looking at a machine you might run windows 95 or xp if retro gaming is your thing. Consider the difficulty of sourcing working PATA drives, DDR2 memory, etc. Also, if it is an AIO and uses a nonstandard power cable to the motherboard or doesn't have standard pinouts for power/reset switch, pc speaker, etc, you'd have to source another case, power supply, and cables particular to that model for testing if it doesnt work.
If it DOES have standard connectors, and PCIe and sata ports, then a Wolfdale Core 2 Duo might be considered marginal at best for 1024x768 resolution, and may not support the ram amounts you want, or really benefit from a ssd r/t not being sata 3, and possibly not being properly setup even for sata2 depending on manufacturer.
You'll need to look on the motherboard for model and pull the heatsink to see what CPU you have.
You'll also need to source drivers for everything, and an OS appropriate to the hardware once you do identify it.