It's a much simpler job than what it looks like at first.
Just remember that the key is flux. You could buy another board, sure, but then what did you learn? Plus, if you're already thinking about buying another board, it means this board is perfect for learning... Buy flux (flux is a transparent grease used for helping the solder flow better), then apply the flux on all the solder joints and then you simply heat the joints with your soldering iron. If you have a flat tip for that soldering iron all the better, because the flat tip will absorb the excess solder.
Then, after using the flux like I described above, you will be able to see that this is the via (the connection) that you need to restore. You can scrape the green "paint" to expose the copper so that you can solder a wire if you need to.