(Sometimes this needs to be said)
I can, you can't.
I wouldn't, though, since the amount of work involved is higher than the cost of a new board.
But here's the positive: You _can_ get good at (de)soldering. It requires studying some theory (there are excellent solder technique videos on youtube) and a lot of practice. You need to understand how a PCB is put together (old and new .. ) to understand what happens when soldering and why a via suddenly "disappears".
You seem to have a lot of the right equipment, so while I agree with everyone else that this board isn't likely to boot again, you can definitely use it to train with.
/Troed