I'm a desktop. That's the only question I can answer. I don't know much about Windows so I don't know how to figure out what a processor number or a motherboard number is. How do I find that?
Who made your desktop? It has to have a model number.
What operating system are you currently using?
Download, run, and attach the results of this utility:
None of the hardware on your PC is supported on windows 10. You have a Q43 Express Chipset which means you are using the Microsoft generic driver.
Ok, you want a graphics card. With hardware this old, compatibility is going to be the issue. And, because you have a sff (small form factor) pc, you cannot use full-height graphics cards, even if you do have a slot available.
My recommendation: Backup your data, and take this PC to a recycle facility. Then, purchase yourself a new(er) machine that is supported on Windows 10.
Also, if you do decide to keep this relic, here is information on it:
You will notice in the "Graphics" section some graphics cards from way back then that you could use: