When you are talking about "another arduino board", is this now a separate board other than the one I discharged the capacitor on?
Yes, if you don't get a chip with a bootloader already on it.
Can this other arduino also be a UNO rev3?
Yes it can.
And when I have this other arduino board is the burning of the bootloader done by the areduino software?
There are a number of ways of doing it. I describe one here:http://www.gammon.com.au/forum/?id=11635
You just need a second board, 6 hook-up wires, and you load the "programming" sketch onto the second (good) board.