Hello there, welcome to the forum.
It is difficult to understand what you've actually done, from what I've gathered you found a spare USB Header from the Case and found some pins on the motherboard with a similar pin-out to that of the USB Header, and tried to connect two correct? However, when you attempted to put the USB Header onto these pins you found neither was compatible but proceeded to shove the USB Header onto the pins and now your computer obviously isn't working yes?
Best course of action:
1) Disassemble the computer. We'll need you to take the motherboard out, and clear out the case so you can return both. (If you're not confident on disassembling your computer, here is a simple pleasant guide: https://www.instructables.com/id/Disassemble-a-Computer/)
2) The main things we want is the motherboard and case to return them (Since you've probably broken both) Once you have both you should return them to were you brought it from for a replacement (If they allow you to do considering you're at fault for the damage and not shipping/the stuff itself).
3) Reassemble the computer. There are literal millions of YouTube videos, magazines and guides in thousands of languages if you get stuck on how to build the computer. Make sure to follow what they say carefully, so you don't repeat the same mistake you just have!
4) Tell us how it goes - any issues, then come back to forums like this or go to the component makers.
Hope this helps a bit