Gorillafunk

I have a 2005 OG Xbox that started to not turn on a little while ago. I pulled it apart and well...it was a bit of a mess. The photos will show a hell of a lot of dust build up. I bought it for $10 a few years ago and it was literally caked in dirt on the outside (like someone had buried it). Anyway I gave it a wipe on the outside and despite the disk tray needing to be 'popped out' each time it worked reliably. But now it doesn't turn on at all. Now I am assuming I should replace those leaking capacitors. But I've never soldered before so a bit wary. What do you think, is that the power problem? Or could the massive dust build up have killed something else. Is it worth giving a clean and putting back together with the capacitators left alone?