I shorted 10V and ground by mistake at the 10V input (connected 10V to the ground there)
What 10V input? What exactly did you connect to ground?
Do you mean you applied 10V at the DC plug?
Also, which component would I have spoiled because of this? Is it easy to replace it and repair the board?
Depends on where you applied 10V and where you shorted it.
I don't think that shorting 10V directly at the DC plug would damage anything on the board. It could fry or blow a fuse in your power supply though.
If you connected 10V to the DC plug and shorted the Vin pin to ground you might have killed the D1 diode that sits next to the DC connector.
It should be both cheap and quite easy to replace if that is the case. It's a M7 diode (1n4007).