I'm sorry if i came out too strong. Its just i have seen my fair share of people new to electronics try fix something and end up braking it even more. Turning what used to be simple fix into disaster.. All because they just didn't understand yet. See enough where changing 0.35$ part turns into changing 35$ parts, you get it... And your friends newer understand why it can cost that much in parts...
I honestly thought your objective was to fix it, so you could play it... But clearly i was wrong. Since this is your practice piece, go for it...
Personally i just happen to think there are easier ways to learn electronics then attempting to fix game consoles bad BGA soldering...
Well at least you have learned something already. Always take note of positions of adjustment knobs and trimmers before you touch them...
But then seriously, you need to know whats the voltage you need out of that PSU if your going to adjust it. Otherwise what do you adjust it for? Some digital stuff has strict requirement what that voltage should be.
Re-flowing BGA? Well that's heat issue, how to get enough heat there without damaging components around that BGA chip.. Most people use hot-air soldering station..
Word of advice about thermal paste, you need often less then you think.. I had to learn this hard way few times..