Well, it sounds like you've verified that there is indeed a problem with the power brick, so it seems reasonable to think that all will be well once you fix it.

As to where to start, the most common failure in these things is a blown filter capacitor. These often fail in a visibly obvious way. You may notice that many (perhaps all) of the electrolytics have dimples or crease lines in the top. These are intended to be points of weakness so that if the capacitor shorts out and overheats, it won't explode. Instead, pressure is relieved controllably by breaking those creases. In the process, the top will bulge. A healthy cap will have a ruler-flat top. So the first step is to inspect the caps carefully. I'm willing to bet that you will find a bad cap.