The parts you blew up are mounted on the side of the circuit board you can't see in the photo posted. I can tell by looking at the back that you have a basic transformer/regulator power supply that's doing your ac/dc conversion. If you're lucky, the voltage regulator (or regulators) that are in the DC supply acted as fuses when it smoked, leaving everything else intact. Get those replaced if so, maybe a couple diodes or resistors, and you're off and running. If you're unlucky, you also fried everything inside the thing that runs on 5V and possibly burned up the LED displays as well. In that case, just buy another one.
And burned up parts won't always be visibly burned but if you heard a bang, and smell the smell, it released the magic smoke from something so chances are really good that something is physically damaged. Also, when things get physically damaged, there's often additional damage you can't see.