I would probably start with just a multimeter and test the rack itself, empty, for +12, -12, +5 where they're all supposed to be. If any of them are way out of whack, that's probably your problem. Given your source was only 12v in, it seems unlikely (but not impossible) that it failed in a way that damaged modules, so you probably got lucky there. Plugging them into another rack is a pretty good way to test them, and from what you've described so far i'd probably just be bold and go for it testing the modules (one at a time though) - but keep an eye for obvious trouble as you power it up and be ready to pull the input power quickly if needed!